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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.

40Papers
32Years
60Questions
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 36 60%
Hard 11 18.3%
Easy 7 11.7%
Not classified 6 10%

Question type distribution

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

Multiple Choices 44 73.3%
Subjective 10 16.7%
Numerical Answer Type (NAT) 6 10%

Subject weightage

Top subjects by unique question coverage.

Mathematics
60 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
60 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Parabola
60 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 2 ONLINE
2 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 2020 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
3 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
3 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 2 OFFLINE
2 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
2 Qs
IIT JEE 2007 PAPER 1 OFFLINE
4 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
3 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002 SCREENING
2 Qs
IIT JEE 2001 SCREENING
2 Qs
IIT JEE 2000 SCREENING
2 Qs
IIT JEE 2000
1 Qs
IIT JEE 1999
1 Qs
IIT JEE 1996
2 Qs
IIT JEE 1995
1 Qs
IIT JEE 1995 SCREENING
1 Qs
IIT JEE 1994
2 Qs
IIT JEE 1991
1 Qs
IIT JEE 1982
1 Qs
IIT JEE 1981
1 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 2 ONLINE20242View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20211View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20201View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20192View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20172View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20153View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20142View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20133View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2011 PAPER 2 OFFLINE20112View paper
IIT JEE 2010 PAPER 1 OFFLINE20101View paper
IIT JEE 2009 PAPER 2 OFFLINE20092View paper
IIT JEE 2007 PAPER 1 OFFLINE20074View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200620063View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200420041View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 2002 SCREENING20022View paper
IIT JEE 2001 SCREENING20012View paper
IIT JEE 200020001View paper
IIT JEE 2000 SCREENING20002View paper
IIT JEE 199919991View paper
IIT JEE 199619962View paper
IIT JEE 199519951View paper
IIT JEE 1995 SCREENING19951View paper
IIT JEE 199419942View paper
IIT JEE 199119911View paper
IIT JEE 198219821View paper
IIT JEE 198119811View paper

All Parabola previous year questions

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

1
1981 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1981
Suppose that the normals drawn at three different points on the parabola \({y^2} = 4x\) pass through the point \((h, k)\). Show that \(h>2\).
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2
1982 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1982
\(A\) is point on the parabola \({y^2} = 4ax\). The normal at \(A\) cuts the parabola again at point \(B\). If \(AB\) subtends a right angle at the vertex of the parabola. Find the slope of \(AB\).
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3
1991 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1991
Three normals are drawn from the point \((c, 0)\) to the curve \({y^2} = x.\) Show that \(c\) must be greater than \(1/2\). One normal is always the \(x\)-axis. Find \(c\) for which the other two normals are perpendicular to each other.
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4
1994 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1994
The point of intersection of the tangents at the ends of the latus rectum of the parabola \({y^2} = 4x\) is ...... .
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5
1994 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1994
Through the vertex \(O\) of parabola \({y^2} = 4x\), chords \(OP\) and \(OQ\) are drawn at right angles to one another . Show that for all positions of \(P\), \(PQ\) cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of \(PQ\).
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6
1995 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1995
Show that the locus of a point that divides a chord of slope \(2\) of the parabola \({y^2} = 4x\) internally in the ratio \(1:2\) is a parabola. Find the vertex of this parabola.
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7
1995 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1995 SCREENING
Consider a circle with its centre lying on the focus of the parabola \({y^2} = 2px\) such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is
A
\(\left( {{p \over 2},p} \right)\) or \(\left( {{p \over 2},- p} \right)\)
B
\(\left( { {p \over 2}, {p \over 2}} \right)\)
C
\(\left( -{{p \over 2},p} \right)\)
D
\(\left( { - {p \over 2}, - {p \over 2}} \right)\)
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8
1996 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1996
Points \(A, B\) and \(C\) lie on the parabola \({y^2} = 4ax\). The tangents to the parabola at \(A, B\) and \(C\), taken in pairs, intersect at points \(P, Q\) and \(R\). Determine the ratio of the areas of the triangles \(ABC\) and \(PQR\).
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9
1996 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1996
From a point \(A\) common tangents are drawn to the circle \({x^2} + {y^2} = {a^2}/2\) and parabola \({y^2} = 4ax\). Find the area of the quadrilateral formed by the common tangents, the chord of contact of the circle and the chord of contact of the parabola.
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10
1999 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 1999
The curve described parametrically by \(x = {t^2} + t + 1,\) \(y = {t^2} - t + 1\) represents
A
a pair of straight lines
B
an ellipse
C
a parabola
D
a hyperbola
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11
2000 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2000
Let \({C_1}\) and \({C_2}\) be respectively, the parabolas \({x^2} = y - 1\) and \({y^2} = x - 1\). Let \(P\) be any point on \({C_1}\) and \(Q\) be any point on \({C_2}\). Let \({P_1}\) and \({Q_1}\) be the reflections of \(P\) and \(Q\), respectively, with respect to the line \(y=x\). Prove that \({P_1}\) lies on \({C_2}\), \({Q_1}\) lies on \({C_1}\) and \(PQ \ge\) min \(\left\{ {P{P_1},Q{Q_1}} \right\}\). Hence or otherwise determine points \({P_0}\) and \({Q_0}\) on the parabolas \({C_1}\) and \({C_2}\) respectively such that \({P_0}{Q_0} \le PQ\) for all pairs of points \((P,Q)\) with \(P\) on \({C_1}\) and \(Q\) on \({C_2}\).
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12
2000 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2000 SCREENING
If \(x + y = k\) is normal to \({y^2} = 12x,\) then \(k\) is
A
\(3\)
B
\(9\)
C
\(-9\)
D
\(-3\)
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13
2000 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2000 SCREENING
If the line \(x - 1 = 0\) is the directrix of the parabola \({y^2} - kx + 8 = 0,\) then one of the values of \(k\) is
A
\(1/8\)
B
\(8\)
C
\(4\)
D
\(1/4\)
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14
2001 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2001 SCREENING
The equation of the directrix of the parabola \({y^2} + 4y + 4x + 2 = 0\)
A
\(x = - 1\)
B
\(x = 1\)
C
\(x = - 3/2\)
D
\(x = 3/2\)
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15
2001 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2001 SCREENING
The equation of the common tangent touching the circle \({\left( {x - 3} \right)^2} + {y^2} = 9\) and the parabola \({y^2} = 4x\) above the \(x\)-axis is
A
\(\sqrt {3y} = 3x + 1\)
B
\(\sqrt {3y} = - \left( {x + 3} \right)\)
C
\(\sqrt {3y} = x + 3\)
D
\(\sqrt {3y} = - \left( {3x + 1} \right)\)
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16
2002 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2002 SCREENING
The equation of the common tangent to the curves \({y^2} = 8x\) and \(xy = - 1\) is
A
\(3y = 9x + 2\)
B
\(y = 2x + 1\)
C
\(2y = x + 8\)
D
\(y= x + 2\)
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17
2002 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2002 SCREENING
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola \({y^2} = 4ax\) is another parabola with directrix
A
\(x = -a\)
B
\(x = -a/2\)
C
\(x = 0\)
D
\(x = a/2\)
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18
2003 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2003
Normals are drawn from the point \(P\) with slopes \({m_1}\), \({m_2}\), \({m_3}\) to the parabola \({y^2} = 4x\). If locus of \(P\) with \({m_1}\) \({m_2}\)\(= \alpha\) is a part of the parabola itself then find \(\alpha\).
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19
2003 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2003 SCREENING
The focal chord to \({y^2} = 16x\) is tangent to \({\left( {x - 6} \right)^2} + {y^2} = 2,\) then the possible values of the slope of the chord, are
A
\(\left\{ { - 1,\,1} \right\}\)
B
\(\left\{ { - 2,\,2} \right\}\)
C
\(\left\{ { - 2,\,-1/2} \right\}\)
D
\(\left\{ { 2,\,-1/2} \right\}\)
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20
2004 · Mathematics · Coordinate Geometry · Parabola
IIT JEE 2004
Tangent is drawn to parabola \({y^2} - 2y - 4x + 5 = 0\) at a point \(P\) which cuts the directrix at the point \(Q\). \(A\) point \(R\) is such that it divides \(QP\) externally in the ratio \(1/2:1\). Find the locus of point \(R\)
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Showing 20 of 60 questions