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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.

34Papers
29Years
45Questions
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 25 55.6%
Hard 13 28.9%
Easy 6 13.3%
Not classified 1 2.2%

Question type distribution

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

Multiple Choices 32 71.1%
Subjective 8 17.8%
Numerical Answer Type (NAT) 4 8.9%
Fill in the blanks 1 2.2%

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.

Ellipse
45 Qs

Paper coverage

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

JEE Advanced 2026 Paper 2 Online
1 Qs
JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 2 OFFLINE
3 Qs
IIT JEE 2009 PAPER 1 OFFLINE
3 Qs
IIT JEE 2009 PAPER 2 OFFLINE
2 Qs
IIT JEE 2008 PAPER 1 OFFLINE
2 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 MAINS
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
1 Qs
IIT JEE 2000
1 Qs
IIT JEE 1999
3 Qs
IIT JEE 1998
2 Qs
IIT JEE 1997
1 Qs
IIT JEE 1996
1 Qs
IIT JEE 1995
1 Qs
IIT JEE 1995 SCREENING
1 Qs
IIT JEE 1994
2 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 2 Online20261View paper
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20211View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20181View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20181View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20171View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20162View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2010 PAPER 2 OFFLINE20103View paper
IIT JEE 2009 PAPER 1 OFFLINE20093View paper
IIT JEE 2009 PAPER 2 OFFLINE20092View paper
IIT JEE 2008 PAPER 1 OFFLINE20082View paper
IIT JEE 200520051View paper
IIT JEE 2005 MAINS20051View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 200220021View paper
IIT JEE 200120011View paper
IIT JEE 200020001View paper
IIT JEE 199919993View paper
IIT JEE 199819982View paper
IIT JEE 199719971View paper
IIT JEE 199619961View paper
IIT JEE 199519951View paper
IIT JEE 1995 SCREENING19951View paper
IIT JEE 199419942View paper

All Ellipse previous year questions

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

1
1994 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1994
Let \(E\) be the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) and \(C\) be the circle \({x^2} + {y^2} = 9\). Let \(P\) and \(Q\) be the points \((1, 2)\) and \((2, 1)\) respectively. Then
A
\(Q\) lies inside \(C\) but outside \(E\)
B
\(Q\) lies outside both \(C\) and \(E\)
C
\(P\) lies inside both \(C\) and \(E\)
D
\(P\) lies inside \(C\) but outside \(E\)
Open complete paper
2
1994 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1994
The equation \(2{x^2} + 3{y^2} - 8x - 18y + 35 = k\) represents
A
no locus if \(k > 0\)
B
an ellipse if \(k < 0\)
C
a point if \(k = 0\)
D
a hyperbola if \(k > 0\)
Open complete paper
3
1995 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1995
Let '\(d\)' be the perpendicular distance from the centre of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) to the tangent drawn at a point \(P\) on the ellipse. If \({F_1}\) and \({F_2}\) are the two foci of the ellipse, then show that \({\left( {P{F_1} - P{F_2}} \right)^2} = 4{a^2}\left( {1 - {{{b^2}} \over {{d^2}}}} \right)\).
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4
1995 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1995 SCREENING
The radius of the circle passing through the foci of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1\), and having its centre at \((0, 3)\) is
A
\(4\)
B
\(3\)
C
\(\sqrt {{1 \over 2}}\)
D
\({{7 \over 2}}\)
Open complete paper
5
1996 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1996
An ellipse has eccentricity \({1 \over 2}\) and one focus at the point \(P\left( {{1 \over 2},1} \right)\). Its one directrix is the common tangent, nearer to the point \(P\), to the circle \({x^2} + {y^2} = 1\) and the hyperbol;a \({x^2} - {y^2} = 1\). The equation of the ellipse, in the standard form, is ............
Write your response
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6
1997 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1997
A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Prove that the tangents at P and Q of the ellipse x2 + 2y2 = 6 are at right angles.
Write your response
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7
1998 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1998
If \(P=(x, y)\), \({F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right)\) and \(16{x^2} + 25{y^2} = 400,\) then \(P{F_1} + P{F_2}\) equals
A
\(8\)
B
\(6\)
C
\(10\)
D
\(12\)
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8
1998 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1998
The number of values of \(c\) such that the straight line \(y=4x + c\) touches the curve \(\left( {{x^2}/4} \right) + {y^2} = 1\) is
A
\(0\)
B
\(1\)
C
\(2\)
D
infinite.
Open complete paper
9
1999 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1999
On the ellipse \(4{x^2} + 9{y^2} = 1,\) 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
10
1999 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1999
Consider the family of circles \({x^2} + {y^2} = {r^2},\,\,2 < r < 5\). If in the first quadrant, the common taingent to a circle of this family and the ellipse \(4{x^2} + 25{y^2} = 100\) meets the co-ordinate axes at \(A\) and \(B\), then find the equation of the locus of vthe mid-point of \(AB\).
Write your response
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11
1999 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 1999
Find the co-ordinates of all the points \(P\) on the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\), for which the area of the triangle \(PON\) is maximum, where \(O\) denotes the origin and \(N\), the foot of the perpendicular from \(O\) to the tangent at \(P\).
Write your response
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12
2000 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2000
Let \(ABC\) be an equilateral triangle inscribed in the circle \({x^2} + {y^2} = {a^2}\). Suppose perpendiculars from \(A, B, C\) to the major axis of the ellipse \(x.{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\), \((a>b)\) meets the ellipse respectively, at \(P, Q, R\). so that \(P, Q, R\) lie on the same side of the major axis as \(A, B, C\) respectively. Prove that the normals to the ellipse drawn at the points \(P, Q\) and \(R\) are concurrent.
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13
2001 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2001
Let \(P\) be a point on the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,0 < b < a\). Let the line parallel to \(y\)-axis passing through \(P\) meet the circle \({x^2} + {y^2} = {a^2}\) at the point \(Q\) such that \(P\) and \(Q\) are on the same side of \(x\)-axis. For two positive real numbers \(r\) and \(s\), find the locus of the point \(R\) on \(PQ\) such that \(PR\) : \(RQ = r: s\) as \(P\) varies over the ellipse.
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14
2002 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2002
Prove that, in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.
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15
2003 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2003 SCREENING
The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 5} = 1,\) is
A
\(27/4\) sq. units
B
\(9\) sq. units
C
\(27/2\) sq. units
D
\(27\) sq. units
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16
2004 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2004 SCREENING
If tangents are drawn to the ellipse \({x^2} + 2{y^2} = 2,\) then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is
A
\({1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1\)
B
\({1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1\)
C
\({{{x^2}} \over 2} + {{{y^2}} \over 4} = 1\)
D
\({{{x^2}} \over 4} + {{{y^2}} \over 2} = 1\)
Open complete paper
17
2005 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2005
Find the equation of the common tangent in \({1^{st}}\) quadrant to the circle \({x^2} + {y^2} = 16\) and the ellipse \({{{x^2}} \over {25}} + {{{y^2}} \over 4} = 1\). Also find the length of the intercept of the tangent between the coordinate axes.
Write your response
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18
2005 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2005 MAINS

Find the equation of the common tangent in the first quadrant to the circle \(x^{2}+y^{2}=16\) and the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{4}=1\). Also find the length of the intercept of the tangent between the coordinate axes.

A
\(\frac{14}{\sqrt5}\)
B
\(\frac{5}{\sqrt3}\)
C
\(\frac{14}{\sqrt3}\)
D
\(\frac{15}{\sqrt3}\)
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19
2005 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2005 SCREENING
The minimum area of triangle formed by the tangent to the \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) and coordinate axes is
A
\(ab\) sq. units
B
\({{{{a^2} + {b^2}} \over 2}}\) sq. units
C
\({{{{\left( {a + b} \right)}^2}} \over 2}\) sq. units
D
\({{{a^2} + ab + {b^2}} \over 3}\) sq. units
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20
2008 · Mathematics · Coordinate Geometry · Ellipse
IIT JEE 2008 PAPER 1 OFFLINE
Let \(P\left( {{x_1},{y_1}} \right)\) and \(Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,\) be the end points of the latus rectum of the ellipse \({x^2} + 4{y^2} = 4.\) The equations of parabolas with latus rectum \(PQ\) are :
A
\({x^2} + 2\sqrt 3y = 3 + \sqrt 3\)
B
\({x^2} - 2\sqrt 3y = 3 + \sqrt 3\)
C
\({x^2} + 2\sqrt 3y = 3 - \sqrt 3\)
D
\({x^2} - 2\sqrt 3 y = 3 - \sqrt 3\)
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Showing 20 of 45 questions