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Previous year question hub

Ellipse - Coordinate Geometry - Mathematics Previous Year Questions

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

109Papers
21Years
117Questions
1Topics

Ellipse question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 93 79.5%
Hard 15 12.8%
Easy 9 7.7%

Question type distribution

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

Multiple Choices 103 88%
Numerical Answer Type (NAT) 14 12%

Subject weightage

Top subjects by unique question coverage.

Mathematics
117 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
117 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Ellipse
117 Qs

Paper coverage

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

JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT
2 Qs
JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE Main 2026 (Online) 2nd April Morning Shift
1 Qs
JEE Main 2026 (Online) 4th April Evening Shift
1 Qs
JEE Main 2026 (Online) 4th April Morning Shift
1 Qs
JEE Main 2026 (Online) 5th April Morning Shift
1 Qs
JEE Main 2026 (Online) 6th April Evening Shift
1 Qs
JEE Main 2026 (Online) 8th April Evening Shift
1 Qs
JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING 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 EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT
1 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 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
1 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 11TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT
1 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 JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY MORNING 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 29TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
2 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
2 Qs
JEE Main 2021 (Online) 25th February Evening Shift
1 Qs
JEE Main 2021 (Online) 26th February Evening Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 4TH 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 EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING 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 10TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL 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 2018 ONLINE 16TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 OFFLINE
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 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2015 OFFLINE
1 Qs
JEE MAIN 2014 OFFLINE
1 Qs
JEE MAIN 2013 OFFLINE
1 Qs
AIEEE 2012
2 Qs
AIEEE 2011
1 Qs
AIEEE 2009
1 Qs
AIEEE 2008
1 Qs
AIEEE 2006
1 Qs
AIEEE 2005
1 Qs
AIEEE 2004
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) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 4th April Evening Shift20261View paper
JEE Main 2026 (Online) 4th April Morning Shift20261View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE Main 2026 (Online) 6th April Evening Shift20261View paper
JEE Main 2026 (Online) 8th April Evening Shift20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING 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 EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 25th February Evening Shift20211View paper
JEE Main 2021 (Online) 26th February Evening Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH 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 EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING 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 APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20191View 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 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
JEE MAIN 2017 OFFLINE20171View paper
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20171View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20161View paper
JEE MAIN 2015 OFFLINE20151View paper
JEE MAIN 2014 OFFLINE20141View paper
JEE MAIN 2013 OFFLINE20131View paper
AIEEE 201220122View paper
AIEEE 201120111View paper
AIEEE 200920091View paper
AIEEE 200820081View paper
AIEEE 200620061View paper
AIEEE 200520051View paper
AIEEE 200420041View paper

All Ellipse previous year questions

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

1
2004 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2004
The eccentricity of an ellipse, with its centre at the origin, is \({1 \over 2}\). If one of the directrices is \(x=4\), then the equation of the ellipse is :
A
\(4{x^2} + 3{y^2} = 1\)
B
\(3{x^2} + 4{y^2} = 12\)
C
\(4{x^2} + 3{y^2} = 12\)
D
\(3{x^2} + 4{y^2} = 1\)
Open complete paper
2
2005 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2005
An ellipse has \(OB\) as semi minor axis, \(F\) and \(F\)' its focii and theangle \(FBF\)' is a right angle. Then the eccentricity of the ellipse is :
A
\({1 \over {\sqrt 2 }}\)
B
\({1 \over 2}\)
C
\({1 \over 4}\)
D
\({1 \over {\sqrt 3 }}\)
Open complete paper
3
2006 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2006
In the ellipse, the distance between its foci is \(6\) and minor axis is \(8\). Then its eccentricity is :
A
\({3 \over 5}\)
B
\({1 \over 2}\)
C
\({4 \over 5}\)
D
\({1 \over {\sqrt 5 }}\)
Open complete paper
4
2008 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2008
A focus of an ellipse is at the origin. The directrix is the line \(x=4\) and the eccentricity is \({{1 \over 2}}\). Then the length of the semi-major axis is :
A
\({{8 \over 3}}\)
B
\({{2 \over 3}}\)
C
\({{4 \over 3}}\)
D
\({{5 \over 3}}\)
Open complete paper
5
2009 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2009
The ellipse \({x^2} + 4{y^2} = 4\) is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the point \((4,0)\). Then the equation of the ellipse is :
A
\({x^2} + 12{y^2} = 16\)
B
\(4{x^2} + 48{y^2} = 48\)
C
\(4{x^2} + 64{y^2} = 48\)
D
\({x^2} + 16{y^2} = 16\)
Open complete paper
6
2011 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2011
Equation of the ellipse whose axes of coordinates and which passes through the point \((-3,1)\) and has eccentricity \(\sqrt {{2 \over 5}}\) is :
A
\(5{x^2} + 3{y^2} - 48 = 0\)
B
\(3{x^2} + 5{y^2} - 15 = 0\)
C
\(5{x^2} + 3{y^2} - 32 = 0\)
D
\(3{x^2} + 5{y^2} - 32 = 0\)
Open complete paper
7
2012 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2012
STATEMENT-1 : An equation of a common tangent to the parabola \({y^2} = 16\sqrt 3 x\) and the ellipse \(2{x^2} + {y^2} = 4\) is \(y = 2x + 2\sqrt 3\)

STATEMENT-2 :If line \(y = mx + {{4\sqrt 3 } \over m},\left( {m \ne 0} \right)\) is a common tangent to the parabola \({y^2} = 16\sqrt {3x}\)and the ellipse \(2{x^2} + {y^2} = 4\), then \(m\) satisfies \({m^4} + 2{m^2} = 24\)

A
Statement-1 is false, Statement-2 is true.
B
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D
Statement-1 is true, Statement-2 is false.
Open complete paper
8
2012 · Mathematics · Coordinate Geometry · Ellipse
AIEEE 2012
An ellipse is drawn by taking a diameter of thec circle \({\left( {x - 1} \right)^2} + {y^2} = 1\) as its semi-minor axis and a diameter of the circle \({x^2} + {\left( {y - 2} \right)^2} = 4\) is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :
A
\(4{x^2} + {y^2} = 4\)
B
\({x^2} + 4{y^2} = 8\)
C
\(4{x^2} + {y^2} = 8\)
D
\({x^2} + 4{y^2} = 16\)
Open complete paper
9
2013 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2013 OFFLINE
The equation of the circle passing through the foci of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1\), and having centre at \((0,3)\) is :
A
\({x^2} + {y^2} - 6y - 7 = 0\)
B
\({x^2} + {y^2} - 6y + 7 = 0\)
C
\({x^2} + {y^2} - 6y - 5 = 0\)
D
\({x^2} + {y^2} - 6y + 5 = 0\)
Open complete paper
10
2014 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2014 OFFLINE
The locus of the foot of perpendicular drawn from the centre of the ellipse \({x^2} + 3{y^2} = 6\) on any tangent to it is :
A
\(\left( {{x^2} + {y^2}} \right) ^2 = 6{x^2} + 2{y^2}\)
B
\(\left( {{x^2} + {y^2}} \right) ^2 = 6{x^2} - 2{y^2}\)
C
\(\left( {{x^2} - {y^2}} \right) ^2 = 6{x^2} + 2{y^2}\)
D
\(\left( {{x^2} - {y^2}} \right) ^2 = 6{x^2} - 2{y^2}\)
Open complete paper
11
2015 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2015 OFFLINE
The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 5} = 1\), is :
A
\({{27 \over 2}}\)
B
\(27\)
C
\({{27 \over 4}}\)
D
\(18\)
Open complete paper
12
2016 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
If the tangent at a point on the ellipse \({{{x^2}} \over {27}} + {{{y^2}} \over 3} = 1\) meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :
A
\({9 \over 2}\)
B
\(3\sqrt 3\)
C
\(9\sqrt 3\)
D
9
Open complete paper
13
2017 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2017 OFFLINE
The eccentricity of an ellipse whose centre is at the origin is \({1 \over 2}\). If one of its directrices is x = – 4, then the equation of the normal to it at \(\left( {1,{3 \over 2}} \right)\) is :
A
2y – x = 2
B
4x – 2y = 1
C
4x + 2y = 7
D
x + 2y = 4
Open complete paper
14
2017 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is \({3 \over 5}\) and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :
A
8
B
32
C
80
D
40
Open complete paper
15
2017 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is :
A
\({1 \over 2}\)
B
\({2 \over {\sqrt 5 }}\)
C
\({{\sqrt 3 } \over 2}\)
D
\({{\sqrt 3 } \over 4}\)
Open complete paper
16
2018 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is \({3 \over 2}\) units, then its eccentricity is :
A
\({1 \over 2}\)
B
\({1 \over 3}\)
C
\({2 \over 3}\)
D
\({1 \over 9}\)
Open complete paper
17
2019 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
The tangent and normal to the ellipse 3x2 + 5y2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is :
A
\({{14} \over 3}\)
B
\({{16} \over 3}\)
C
\({{68} \over {15}}\)
D
\({{34} \over {15}}\)
Open complete paper
18
2019 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
If the line x – 2y = 12 is tangent to the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) at the point \(\left( {3, - {9 \over 2}} \right)\) , then the length of the latus rectum of the ellipse is :
A
5
B
9
C
\(8\sqrt 3\)
D
\(12\sqrt 2\)
Open complete paper
19
2019 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
Let S = \(\left\{ {\left( {x,y} \right) \in {R^2}:{{{y^2}} \over {1 + r}} - {{{x^2}} \over {1 - r}}} \right\};r \ne \pm 1.\) Then S represents :
A
an ellipse whose eccentricity is \({1 \over {\sqrt {r + 1} }},\) where r > 1
B
an ellipse whose eccentricity is \({2 \over {\sqrt {r + 1} }},\) where 0 < r < 1
C
an ellipse whose eccentricity is \({2 \over {\sqrt {r - 1} }},\) where 0 < r < 1
D
an ellipse whose eccentricity is \(\sqrt {{2 \over {r + 1}}}\), where r > 1
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20
2019 · Mathematics · Coordinate Geometry · Ellipse
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?
A
\(\left( {4\sqrt 2 ,2\sqrt 3 } \right)\)
B
\(\left( {4\sqrt 3 ,2\sqrt 3 } \right)\)
C
\(\left( {4\sqrt 3 ,2\sqrt 2 } \right)\)
D
\(\left( {4\sqrt 2 ,2\sqrt 2 } \right)\)
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