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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.

15Papers
14Years
34Questions
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.

Not classified 36 100%

Question type distribution

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

Multiple Choices 36 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
34 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
34 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Ellipse
34 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
WB JEE 2024
3 Qs
WB JEE 2023
3 Qs
WB JEE 2022
2 Qs
WB JEE 2021
2 Qs
WB JEE 2020
4 Qs
WB JEE 2019
2 Qs
WB JEE 2018
1 Qs
WB JEE 2017
2 Qs
WB JEE 2016
4 Qs
WB JEE 2011
2 Qs
WB JEE 2010
1 Qs
WB JEE 2009
3 Qs
WB JEE 2008
3 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
WB JEE 202420243View paper
WB JEE 202320233View paper
WB JEE 202220222View paper
WB JEE 202120212View paper
WB JEE 202020204View paper
WB JEE 201920192View paper
WB JEE 201820181View paper
WB JEE 201720172View paper
WB JEE 201620164View paper
WB JEE 201120112View paper
WB JEE 201020101View paper
WB JEE 200920093View paper
WB JEE 200820083View paper

All Ellipse previous year questions

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

1
2016 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2016
The line y = x + \(\lambda\) is tangent to the ellipse 2x2 + 3y2 = 1. Then, \(\lambda\) is
A
\(-\)2
B
1
C
\(\sqrt {{5 \over 6}}\)
D
\(\sqrt {{2 \over 3}}\)
Open complete paper
2
2016 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2016
The equation of auxiliary circle of the ellipse \(16{x^2} + 25{y^2} + 32x - 100y = 284\) is
A
\({x^2} + {y^2} + 2x - 4y - 20 = 0\)
B
\({x^2} + {y^2} + 2x - 4y = 0\)
C
\({(x + 1)^2} + {(y - 2)^2} = 400\)
D
\({(x + 1)^2} + {(y - 2)^2} = 255\)
Open complete paper
3
2016 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2016
On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y, are
A
\(\left( {{2 \over 5},{1 \over 5}} \right)\)
B
\(\left( { - {2 \over 5},{1 \over 5}} \right)\)
C
\(\left( { - {2 \over 5}, - {1 \over 5}} \right)\)
D
\(\left( {{2 \over 5}, - {1 \over 5}} \right)\)
Open complete paper
4
2016 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2016
The points of the ellipse 16x2 + 9y2 = 400 at which the ordinate decreases at the same rate at which the abscissa increases is/are given by
A
\(\left( {3,{{16} \over 3}} \right)\left( { - 3, - {{16} \over 3}} \right)\)
B
\(\left( {3, - {{16} \over 3}} \right)\left( { - 3,{{16} \over 3}} \right)\)
C
\(\left( {{1 \over {16}},{1 \over 9}} \right)\left( { - {1 \over {16}}, - {1 \over 9}} \right)\)
D
\(\left( {{1 \over {16}}, - {1 \over 9}} \right)\left( { - {1 \over {16}},{1 \over 9}} \right)\)
Open complete paper
5
2017 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2017
Tangents are drawn to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 5} = 1\) at the ends of both latusrectum. The area of the quadrilateral, so formed is
A
27 sq units
B
\({{13} \over 2}\) sq units
C
\({{15} \over 4}\) sq units
D
45 sq units
Open complete paper
6
2017 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2017
B is an extremity of the minor axis of an ellipse whose foci are S and S'. If \(\angle SBS'\) is a right angle, then the eccentricity of the ellipse is
A
\({1 \over 2}\)
B
\({1 \over {\sqrt 2 }}\)
C
\({2 \over 3}\)
D
\({1 \over 3}\)
Open complete paper
7
2018 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2018
Let P be a point on the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) and the line through P parallel to the Y-axis meets the circle x2 + y2 = 9 at Q, where P, Q are on the same side of the X-axis. If R is a point on PQ such that \({{PR} \over {RQ}} = {1 \over 2}\), then the locus of R is
A
\({{{x^2}} \over 9} + {{9{y^2}} \over {49}} = 1\)
B
\({{{x^2}} \over {49}} + {{{y^2}} \over 9} = 1\)
C
\({{{x^2}} \over 9} + {{{y^2}} \over {49}} = 1\)
D
\({{9{x^2}} \over {49}} + {{{y^2}} \over 9} = 1\)
Open complete paper
8
2019 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2019
P is the extremity of the latusrectum of ellipse \(3{x^2} + 4{y^2} = 48\) in the first quadrant. The eccentric angle of P is
A
\({\pi \over 8}\)
B
\({{3\pi } \over 4}\)
C
\({\pi \over 3}\)
D
\({{2\pi } \over 3}\)
Open complete paper
9
2019 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2019
S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentricity of the ellipse is
A
\({1 \over 4}\)
B
\({1 \over 3}\)
C
\({1 \over 2}\)
D
\({2 \over 3}\)
Open complete paper
10
2020 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2020
If B and B' are the ends of minor axis and S and S' are the foci of the ellipse \({{{x^2}} \over {25}} + {{{y^2}} \over 9} = 1\), then the area of the rhombus SBS' B' will be
A
12 sq units
B
48 sq units
C
24 sq units
D
36 sq units
Open complete paper
11
2020 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2020
Consider the curve \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\). The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of
A
\({\pi \over 4}\)
B
\({\pi \over 3}\)
C
\({\pi \over 2}\)
D
\({\pi \over 6}\)
Open complete paper
12
2020 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2020
Consider a tangent to the ellipse \({{{x^2}} \over 2} + {{{y^2}} \over 1} = 1\) at any point. The locus of the mid-point of the portion intercepted between the axes is
A
\({{{x^2}} \over 2} + {{{y^2}} \over 4} = 1\)
B
\({{{x^2}} \over 4} + {{{y^2}} \over 2} = 1\)
C
\({1 \over {3{x^2}}} + {1 \over {4{y^2}}} = 1\)
D
\({1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1\)
Open complete paper
13
2020 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2020
Consider the curve \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\). The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of
A
\({\pi \over 4}\)
B
\({\pi \over 3}\)
C
\({\pi \over 2}\)
D
\({\pi \over 6}\)
Open complete paper
14
2021 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2021
The co-ordinate of a point on the auxiliary circle of the ellipse x2 + 2y2 = 4 corresponding to the point on the ellipse whose eccentric angle is 60\(^\circ\) will be
A
\((\sqrt 3 ,1)\)
B
\((1,\sqrt 3 )\)
C
(1, 1)
D
(1, 2)
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15
2021 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2021
The points of intersection of two ellipses \({x^2} + 2{y^2} - 6x - 12y + 20 = 0\) and \(2{x^2} + {y^2} - 10x - 6y + 15 = 0\) lie on a circle. The centre of the circle is
A
(8, 3)
B
(8, 1)
C
\(\left( {{8 \over 3},3} \right)\)
D
(3, 8)
Open complete paper
16
2022 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2022

AB is a variable chord of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\). If AB subtends a right angle at the origin O, then \({1 \over {O{A^2}}} + {1 \over {O{B^2}}}\) equals to

A
\({1 \over {{a^2}}} + {1 \over {{b^2}}}\)
B
\({1 \over {{a^2}}} - {1 \over {{b^2}}}\)
C
\({a^2} + {b^2}\)
D
\({a^2} - {b^2}\)
Open complete paper
17
2022 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2022

Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

A
a circle
B
a parabola
C
an ellipse
D
a hyperbola
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18
2023 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2023

The tangent at point \((a\cos \theta ,b\sin \theta ),0 < \theta < {\pi \over 2}\), to the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) meets the x-axis at T and y-axis at T\(_1\). Then the value of \(\mathop {\min }\limits_{0 < \theta < {\pi \over 2}} (OT)(O{T_1})\) is

A
ab
B
2ab
C
0
D
1
Open complete paper
19
2023 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2023

Let f be a strictly decreasing function defined on R such that \(f(x) > 0,\forall x \in R\). Let \({{{x^2}} \over {f({a^2} + 5a + 3)}} + {{{y^2}} \over {f(a + 15)}} = 1\) be an ellipse with major axis along the y-axis. The value of 'a' can lie in the interval (s)

A
\(( - \infty , - 6)\)
B
\(( - 6,2)\)
C
\((2,\infty )\)
D
\(( - \infty ,\infty )\)
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20
2023 · Mathematics · Coordinate Geometry · Ellipse
WB JEE 2023

If the lines joining the focii of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) where \(a > b\), and an extremity of its minor axis is inclined at an angle 60\(^\circ\), then the eccentricity of the ellipse is

A
\({{\sqrt 3 } \over 2}\)
B
\({1 \over 2}\)
C
\({{\sqrt 7 } \over 3}\)
D
\({1 \over {\sqrt 3 }}\)
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Showing 20 of 34 questions