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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.

16Papers
14Years
45Questions
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.

Not classified 47 100%

Question type distribution

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

Multiple Choices 44 93.6%
Subjective 3 6.4%

Subject weightage

Top subjects by unique question coverage.

Mathematics
45 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
45 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Parabola
45 Qs

Paper coverage

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

WB JEE 2026
2 Qs
WB JEE 2026
2 Qs
VITEEE 2025
3 Qs
WB JEE 2025
1 Qs
WB JEE 2024
1 Qs
WB JEE 2023
3 Qs
WB JEE 2022
7 Qs
WB JEE 2021
2 Qs
WB JEE 2020
3 Qs
WB JEE 2018
5 Qs
WB JEE 2017
3 Qs
WB JEE 2016
3 Qs
WB JEE 2011
3 Qs
WB JEE 2010
1 Qs
WB JEE 2009
2 Qs
WB JEE 2008
6 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
WB JEE 202620262View paper
WB JEE 202620262View paper
VITEEE 202520253View paper
WB JEE 202520251View paper
WB JEE 202420241View paper
WB JEE 202320233View paper
WB JEE 202220227View paper
WB JEE 202120212View paper
WB JEE 202020203View paper
WB JEE 201820185View paper
WB JEE 201720173View paper
WB JEE 201620163View paper
WB JEE 201120113View paper
WB JEE 201020101View paper
WB JEE 200920092View paper
WB JEE 200820086View paper

All Parabola previous year questions

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

1
2016 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2016
If the vertex of the conic \({y^2} - 4y = 4x - 4a\) always lies between the straight lines \(x + y = 3\) and \(2x + 2y - 1 = 0\), then
A
\(2 < a < 4\)
B
\(- {1 \over 2} < a < 2\)
C
\(0 < a < 2\)
D
\(- {1 \over 2} < a < {3 \over 2}\)
Open complete paper
2
2016 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2016
The locus of the mid-points of all chords of the parabola y2 = 4ax through its vertex is another parabola with directrix
A
x = \(-\) a
B
x = a
C
x = 0
D
x = \(-\) \({a \over 2}\)
Open complete paper
3
2016 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2016
A line passing through the point of intersection of x + y = 4 and x \(-\) y = 2 makes an angle \({\tan ^{ - 1}}\left( {{3 \over 4}} \right)\) with the X-axis. It intersects the parabola \({y^2} = 4(x - 3)\) at points \(({x_1},{y_1})\) and \(({x_2},{y_2})\), respectively. Then, \(|{x_1},{y_2}|\) is equal to
A
\({{16} \over 9}\)
B
\({{32} \over 9}\)
C
\({{40} \over 9}\)
D
\({{80} \over 9}\)
Open complete paper
4
2017 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2017
The focus of the conic x2 \(-\) 6x + 4y + 1 = 0 is
A
(2, 3)
B
(3, 2)
C
(3, 1)
D
(1, 4)
Open complete paper
5
2017 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2017
If the tangent to \({y^2} = 4ax\) at the point \((a{t^2},2at)\) where | t | > 1 is a normal to \({x^2} - {y^2} = {a^2}\) at the point \((a\sec \theta ,a\tan \theta )\), then
A
\(t = - \cos ec\theta\)
B
\(t = - \sec \theta\)
C
\(t = 2\tan \theta\)
D
\(t = 2\cot \theta\)
Open complete paper
6
2017 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2017
The axis of the parabola \({x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0\) is
A
\(x + y = 0\)
B
\(x + y - 1 = 0\)
C
\(x - y + 1 = 0\)
D
\(x - y = {1 \over {\sqrt 2 }}\)
Open complete paper
7
2018 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2018
Number of common tangents of y = x2 and y = \(-\)x2 + 4x \(-\) 4 is
A
1
B
2
C
3
D
4
Open complete paper
8
2018 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2018
Let A, B the two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is
A
\(- {1 \over r}\)
B
\({1 \over r}\)
C
\({2 \over r}\)
D
\(- {2 \over r}\)
Open complete paper
9
2018 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2018
Let P(at2, 2at), Q, R(ar2, 2ar) be three points on a parabola y2 = 4ax. If PQ is the focal chord and PK, QR are parallel where the co-ordinates of K is (2a, 0), then the value of r is
A
\({t \over {1 - {t^2}}}\)
B
\({{1 - {t^2}} \over 1}\)
C
\({{{{t^2} + 1} \over t}}\)
D
\({{{{t^2} - 1} \over t}}\)
Open complete paper
10
2018 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2018
Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P(4, \(-\) 4) and Q(9, 6). Let R be a point on the arc of the parabola between P and Q. Then, the area of \(\Delta\)PQR is largest when
A
\(\angle\)PQR = 90\(^\circ\)
B
R(4, 4)
C
R\(\left( {{1 \over 4},1} \right)\)
D
R\(\left( {1,{1 \over 4}} \right)\)
Open complete paper
11
2018 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2018
The area of the region lying above X-axis, and included between the circle x2 + y2 = 2ax and the parabola y2 = ax, a > 0 is
A
8\(\pi\)a2
B
\({a^2}\left( {{\pi \over 4} - {2 \over 3}} \right)\)
C
\({{16\pi {a^2}} \over 9}\)
D
\(\pi \left( {{{27} \over 8} + 3{a^2}} \right)\)
Open complete paper
12
2020 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2020
If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through (\(-\)1, 0), then
A
a = b = \(-\)1, c = 3
B
a = b = \({1 \over 2}\), c = 0
C
a = c = \({1 \over 4}\), b = \({1 \over 2}\)
D
a = 0, b = c = \({1 \over 2}\)
Open complete paper
13
2020 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2020
The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. Then, the length of the latusrectum is
A
\(4\sqrt 2\) units
B
\(2\sqrt 2\) units
C
8 units
D
\(8\sqrt 2\) units
Open complete paper
14
2020 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2020
The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle \(\alpha\) with the axis of the parabola is
A
\(\pm\) 4a cot \(\alpha\) cosec \(\alpha\)
B
4a cot \(\alpha\) cosec \(\alpha\)
C
\(-\) 4a cot \(\alpha\) cosec \(\alpha\)
D
4a cosec2 \(\alpha\)
Open complete paper
15
2021 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2021
From a point (d, 0) three normal are drawn to the parabola y2 = x, then
A
d = \({1 \over 2}\)
B
d > \({1 \over 2}\)
C
d < \({1 \over 2}\)
D
d = \({1 \over 3}\)
Open complete paper
16
2021 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2021
The locus of the vertices of the family of parabolas \(6y = 2{a^3}{x^2} + 3{a^2}x - 12a\) is
A
\(xy = {{105} \over {64}}\)
B
\(xy = {{64} \over {105}}\)
C
\(xy = {{35} \over {16}}\)
D
\(xy = {{16} \over {35}}\)
Open complete paper
17
2022 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2022

The point of contact of the tangent to the parabola y2 = 9x which passes through the point (4, 10) and makes an angle \(\theta\) with the positive side of the axis of the parabola where tan\(\theta\) > 2, is

A
\(\left( {{4 \over 9},2} \right)\)
B
(4, 6)
C
(4, 5)
D
\(\left( {{1 \over 4},{1 \over 6}} \right)\)
Open complete paper
18
2022 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2022

A line passes through the point \(( - 1,1)\) and makes an angle \({\sin ^{ - 1}}\left( {{3 \over 5}} \right)\) in the positive direction of x-axis. If this line meets the curve \({x^2} = 4y - 9\) at A and B, then |AB| is equal to

A
\({4 \over 5}\) unit
B
\({5 \over 4}\) unit
C
\({3 \over 5}\) unit
D
\({5 \over 3}\) unit
Open complete paper
19
2022 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2022

AB is a chord of a parabola y2 = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

A
a unit
B
2a unit
C
8a unit
D
4a unit
Open complete paper
20
2022 · Mathematics · Coordinate Geometry · Parabola
WB JEE 2022

From the point (\(-\)1, \(-\)6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is

A
\(\pi\)/3
B
\(\pi\)/4
C
\(\pi\)/6
D
\(\pi\)/2
Open complete paper

Showing 20 of 45 questions