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Previous year question hub

Parabola - Coordinate Geometry - Mathematics Previous Year Questions

Practice Parabola - Coordinate Geometry - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

130Papers
22Years
155Questions
1Topics

Parabola question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Parabola. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 122 78.7%
Hard 22 14.2%
Easy 11 7.1%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 122 78.7%
Numerical Answer Type (NAT) 33 21.3%

Subject weightage

Top subjects by unique question coverage.

Mathematics
155 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
155 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Parabola
155 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Main 2026 (Online) 6th April Morning Shift
2 Qs
JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT
2 Qs
JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE Main 2026 (Online) 4th April Evening Shift
1 Qs
JEE Main 2026 (Online) 5th April Evening Shift
1 Qs
JEE Main 2026 (Online) 8th April Evening Shift
1 Qs
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT
3 Qs
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT
1 Qs
JEE Main 2021 (Online) 25th February Evening Shift
2 Qs
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT
2 Qs
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
2 Qs
JEE Main 2021 (Online) 24th February Evening Shift
1 Qs
JEE Main 2021 (Online) 24th February Morning Shift
1 Qs
JEE Main 2021 (Online) 25th February Morning Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT
2 Qs
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 6TH SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT
3 Qs
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
2 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
2 Qs
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2018 OFFLINE
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2016 OFFLINE
1 Qs
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2015 OFFLINE
1 Qs
JEE MAIN 2014 OFFLINE
1 Qs
JEE MAIN 2013 OFFLINE
1 Qs
AIEEE 2010
1 Qs
AIEEE 2008
1 Qs
IIT-JEE 2007
4 Qs
AIEEE 2007
1 Qs
AIEEE 2006
1 Qs
AIEEE 2005
1 Qs
AIEEE 2004
1 Qs
AIEEE 2003
1 Qs
AIEEE 2002
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Evening Shift20261View paper
JEE Main 2026 (Online) 4th April Evening Shift20261View paper
JEE Main 2026 (Online) 5th April Evening Shift20261View paper
JEE Main 2026 (Online) 6th April Morning Shift20262View paper
JEE Main 2026 (Online) 8th April Evening Shift20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT20243View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20242View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Evening Shift20211View paper
JEE Main 2021 (Online) 24th February Morning Shift20211View paper
JEE Main 2021 (Online) 25th February Evening Shift20212View paper
JEE Main 2021 (Online) 25th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20193View paper
JEE MAIN 2018 OFFLINE20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20181View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20171View paper
JEE MAIN 2016 OFFLINE20161View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20161View paper
JEE MAIN 2015 OFFLINE20151View paper
JEE MAIN 2014 OFFLINE20141View paper
JEE MAIN 2013 OFFLINE20131View paper
AIEEE 201020101View paper
AIEEE 200820081View paper
AIEEE 200720071View paper
IIT-JEE 200720074View paper
AIEEE 200620061View paper
AIEEE 200520051View paper
AIEEE 200420041View paper
AIEEE 200320031View paper
AIEEE 200220021View paper

All Parabola previous year questions

Practice every matching question in batches of 20, with every available option.

1
2002 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2002
Two common tangents to the circle \({x^2} + {y^2} = 2{a^2}\) and parabola \({y^2} = 8ax\) are :
A
\(x = \pm \left( {y + 2a} \right)\)
B
\(y = \pm \left( {x + 2a} \right)\)
C
\(x = \pm \left( {y + a} \right)\)
D
\(y = \pm \left( {x + a} \right)\)
Open complete paper
2
2003 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2003
The normal at the point\(\left( {bt_1^2,2b{t_1}} \right)\) on a parabola meets the parabola again in the point \(\left( {bt_2^2,2b{t_2}} \right)\), then :
A
\({t_2} = {t_1} + {2 \over {{t_1}}}\)
B
\({t_2} = -{t_1} - {2 \over {{t_1}}}\)
C
\({t_2} = -{t_1} + {2 \over {{t_1}}}\)
D
\({t_2} = {t_1} - {2 \over {{t_1}}}\)
Open complete paper
3
2004 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2004
If \(a \ne 0\) and the line \(2bx+3cy+4d=0\) passes through the points of intersection of the parabolas \({y^2} = 4ax\) and \({x^2} = 4ay\), then :
A
\({d^2} + {\left( {3b - 2c} \right)^2} = 0\)
B
\({d^2} + {\left( {3b + 2c} \right)^2} = 0\)
C
\({d^2} + {\left( {2b - 3c} \right)^2} = 0\)
D
\({d^2} + {\left( {2b + 3c} \right)^2} = 0\)
Open complete paper
4
2005 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2005
Let \(P\) be the point \((1, 0)\) and \(Q\) a point on the parabola \({y^2} = 8x\). The locus of mid point of \(PQ\) is :
A
\({y^2} - 4x + 2 = 0\)
B
\({y^2} + 4x + 2 = 0\)
C
\({x^2} + 4y + 2 = 0\)
D
\({x^2} - 4y + 2 = 0\)
Open complete paper
5
2006 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2006
The locus of the vertices of the family of parabolas
\(y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a\) is :
A
\(xy = {{105} \over {64}}\)
B
\(xy = {{3} \over {4}}\)
C
\(xy = {{35} \over {16}}\)
D
\(xy = {{64} \over {105}}\)
Open complete paper
6
2007 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2007
The equation of a tangent to the parabola \({y^2} = 8x\) is \(y=x+2\). The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is :
A
\((2,4)\)
B
\((-2,0)\)
C
\((-1,1)\)
D
\((0,2)\)
Open complete paper
7
2008 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2008
A parabola has the origin as its focus and the line \(x=2\) as the directrix. Then the vertex of the parabola is at :
A
\((0,2)\)
B
\((1,0)\)
C
\((0,1)\)
D
\((2,0)\)
Open complete paper
8
2010 · Mathematics · Coordinate Geometry · Parabola
AIEEE 2010
If two tangents drawn from a point \(P\) to the parabola \({y^2} = 4x\) are at right angles, then the locus of \(P\) is
A
\(2x+1=0\)
B
\(x=-1\)
C
\(2x-1=0\)
D
\(x=1\)
Open complete paper
9
2013 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2013 OFFLINE
Given : A circle, \(2{x^2} + 2{y^2} = 5\) and a parabola, \({y^2} = 4\sqrt 5 x\).
Statement-1 : An equation of a common tangent to these curves is \(y = x + \sqrt 5\).

Statement-2 : If the line, \(y = mx + {{\sqrt 5 } \over m}\left( {m \ne 0} \right)\) is their common tangent, then \(m\) satiesfies \({m^4} - 3{m^2} + 2 = 0\).

A
Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C
Statement-1 is true; Statement-2 is false.
D
Statement-1 is false Statement-2 is true.
Open complete paper
10
2014 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2014 OFFLINE
The slope of the line touching both the parabolas \({y^2} = 4x\) and \({x^2} = - 32y\) is
A
\({{1 \over 8}}\)
B
\({{2 \over 3}}\)
C
\({{1 \over 2}}\)
D
\({{3 \over 2}}\)
Open complete paper
11
2015 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2015 OFFLINE
Let \(O\) be the vertex and \(Q\) be any point on the parabola, \({{x^2} = 8y}\). If the point \(P\) divides the line segment \(OQ\) internally in the ratio \(1:3\), then locus of \(P\) is :
A
\({y^2} = 2x\)
B
\({{x^2} = 2y}\)
C
\({{x^2} = y}\)
D
\({y^2} = x\)
Open complete paper
12
2016 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2016 OFFLINE
Let \(P\) be the point on the parabola, \({{y^2} = 8x}\) which is at a minimum distance from the centre \(C\) of the circle, \({x^2} + {\left( {y + 6} \right)^2} = 1\). Then the equation of the circle, passing through \(C\) and having its centre at \(P\) is:
A
\({{x^2} + {y^2} - {x \over 4} + 2y - 24 = 0}\)
B
\({{x^2} + {y^2} - 4x + 9y + 18 = 0}\)
C
\({{x^2} + {y^2} - 4x + 8y + 12 = 0}\)
D
\({{x^2} + {y^2} - x + 4y - 12 = 0}\)
Open complete paper
13
2016 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
P and Q are two distinct points on the parabola, y2 = 4x, with parameters t and t1 respectively. If the normal at P passes through Q, then the minimum value of \(t_1^2\) is :
A
2
B
4
C
6
D
8
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14
2017 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
If the common tangents to the parabola, x2 = 4y and the circle, x2 + y2 = 4 intersect at the point P, then the distance of P from the origin, is :
A
\(\sqrt 2 + 1\)
B
2(3 + 2 \(\sqrt 2\))
C
2(\(\sqrt 2\) + 1)
D
3 + 2\(\sqrt 2\)
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15
2017 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then \(\left| c \right|\) is equal to :
A
\(2\sqrt 3\)
B
\(8\sqrt 3\)
C
\(10\sqrt 3\)
D
\(16\sqrt 3\)
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16
2018 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2018 OFFLINE
Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and \(\angle\)CPB = \(\theta\), then a value of tan\(\theta\) is :
A
\({4 \over 3}\)
B
\({1 \over 2}\)
C
2
D
3
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17
2018 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
Tangents drawn from the point (\(-\)8, 0) to the parabola y2 = 8x touch the parabola at \(P\) and \(Q.\) If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :
A
24
B
32
C
48
D
64
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18
2018 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
Two parabolas with a common vertex and with axes along x-axis and \(y\)-axis, respectively intersect each other in the first quadrant. If the length of the latus rectum of each parabola is \(3\), then the equation of the common tangent to the two parabolas is :
A
4(x + y) + 3 = 0
B
3(x + y) + 4 = 0
C
8(2x + y) + 3 = 0
D
x + 2y + 3 = 0
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19
2018 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
Let P be a point on the parabola, x2 = 4y. If the distance of P from the center of the circle, x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P, is :
A
x + 4y \(-\) 2 = 0
B
x \(-\) y + 3 = 0
C
x + y +1 = 0
D
x + 2y = 0
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20
2019 · Mathematics · Coordinate Geometry · Parabola
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
If the line ax + y = c, touches both the curves x2 + y2 = 1 and y2 = 4\(\sqrt 2\)x , then |c| is equal to :
A
2
B
\(\sqrt 2\)
C
\({1 \over {\sqrt 2 }}\)
D
\({1 \over 2}\)
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