Mathematics - Parabola
Practise 35 JEE Advanced previous year questions on Parabola, compiled from papers spanning 2006 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.
Parabola has been asked in 18 of the 27 years of JEE Advanced papers analysed (2000–2026), with 35 questions in all. 20% of them were easy, 69% moderate and 11% tough. Most of its questions came from 2006, with 5 questions that year. In the last three years (2024–2026) it had 4 questions across 6 papers, about 0.7 per paper.
The chapter's 10 topics are not weighted equally: Common Tangent (7 questions, 20%), Tangent to Parabola (7 questions, 20%), and Normal to Parabola (6 questions, 17%) have been asked the most. Over the last five years the most frequent topics have been Normal to Parabola (2), Tangent to Parabola (2), and Chord with given Middle Point (1). Common Tangent has produced the most tough questions (1).
- 1Let be the tangent to the parabola at the point . Let be the tangent to the same parabola at another point on the parabola. If and are perpe2026 (Paper 2)Tangent to Parabola
- 2Let denote the locus of the mid-points of those chords of the parabola , such that the area of the region enclosed between the parabola and 2025 (Paper 2)Chord with given Middle Point
- 3Let be three points in the -plane. Suppose that the lines and are tangents to the curve at and , respectively. If and , then which of the fo2024 (Paper 2)Tangent to Parabola
- 4A normal with slope is drawn from the point to the parabola , where . Let be the line passing through and parallel to the directrix of the p2024 (Paper 2)Normal to Parabola
- 5Let P be a point on the parabola y 2 = 4 a x , where a 0 . The normal to the parabola at P meets the x -axis at a point Q . The area of the 2023 (Paper 1)Normal to Parabola
- 6Consider the parabola y 2 = 4 x . Let S be the focus of the parabola. A pair of tangents drawn to the parabola from the point P = - 2 , 1 me2022 (Paper 1)Pair of Tangents
- 7Let E denote the parabola y 2 = 8 x . Let P = - 2 , 4 , and let Q and Q ' be two distinct points on E such that the lines P Q and P Q ' are 2021 (Paper 2)Properties of Tangent
- 8Consider the region and . Let be the family of all circles that are contained in and have centers on the -axis. Let be the circle that has l2021 (Paper 2)Common Tangent
- 9Consider the region and . Let be the family of all circles that are contained in and have centers on the -axis. Let be the circle that has l2021 (Paper 2)Common Tangent
- 10If a chord, which is not a tangent, of the parabola y 2 = 16 x has the equation 2 x + y = p , and midpoint (h, k), then which of the followi2017 (Paper 1)Chord with given Middle Point
- 11Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. Column 1 Column 2 Column 3 (I) x2017 (Paper 1)Tangent to Parabola
- 12Let P be the point on the parabola y 2 = 4 x which is at the shortest distance from the center S of the circle x 2 + y 2 - 4 x - 16 y + 64 =2016 (Paper 2)Normal to Parabola
- 13If the normal of the parabola y 2 = 4 x drawn at the end points of its latus rectum are tangents to the circle x - 3 2 + y + 2 2 = r 2 , the2015 (Paper 1)Normal to Parabola
- 14Let P and Q be distinct points on the parabola y 2 = 2 x such that a circle with P Q as diameter passes through the vertex O of the parabola2015 (Paper 1)Chord of parabola
- 15Suppose that the foci of the ellipse x 2 9 + y 2 5 = 1 are f 1 , 0 a n d ( f 2 , 0 ) where f 1 0 a n d f 2 0 . Let P 1 a n d P 2 be two para2015 (Paper 2)Tangent to Parabola
- 16The common tangents to the circle x 2 + y 2 = 2 and the parabola y 2 = 8 x touch the circle at the points P, and Q the parabola at the point2014 (Paper 2)Common Tangent
- 17Paragraph: Let be nonzero real numbers. Let and be distinct points on the parabola . Suppose that is the focal chord and lines and are paral2014 (Paper 2)Tangent to Parabola
- 18Paragraph: Let be nonzero real numbers. Let and be distinct points on the parabola . Suppose that is the focal chord and lines and are paral2014 (Paper 2)Tangent to Parabola
- 19Paragraph: Let be a focal chord of the parabola . The tangents to the parabola at and meet at a point lying on the line . Question: Length o2013 (Paper 2)Chord of parabola
- 20Paragraph: Let be a focal chord of the parabola . The tangents to the parabola at and meet at a point lying on the line . Question: If chord2013 (Paper 2)Chord of parabola
- 21Let be the focus of the parabola and let be the common chord of the circle and the given parabola. The area of the triangle is2012 (Paper 1)Chord of parabola
- 22Consider the parabola . Let be the area of the triangle formed by the end points of its latusrectum and the point on the parabola and be the2011 (Paper 1)Properties of Tangent
- 23Let be any point on the parabola . Let be the point that divides the line segment from to in the ratio . Then, the locus of is2011 (Paper 2)Locus
- 24Let be a normal to the parabola . If passes through the point , then is given by2011 (Paper 2)Normal to Parabola
- 25Let and be two distinct points on the parabola . If the axis of the parabola touches a circle of radius having as its diameter, then the slo2010 (Paper 1)Chord of parabola
- 26The tangent and the normal to the parabola at a point on2009 (Paper 2)Tangent to Parabola
- 27Consider the two curves , then2008 (Paper 1)Common Tangent
- 28Paragraph: Consider the circle and the parabola . They intersect at and in the first and the fourth quadrants, respectively. Tangents to the2007 (Paper 1)Common Tangent
- 29Paragraph: Consider the circle and the parabola . They intersect at and in the first and the fourth quadrants, respectively. Tangents to the2007 (Paper 1)Common Tangent
- 30Statement I The curve is symmetric with respect to the line Statement II A parabola is symmetric about its axis.2007 (Paper 2)Reflection property
- 31Axis of a parabola is and vertex and focus are at a distance and respectively, from the origin. Then, equation of the parabola is2006standard equation of parabola
- 32Equation of common tangent of is2006Common Tangent
- 33Paragraph: Read the following passage and answer the questions. Let be a square of side length 2 units. is the circle through vertices and i2006standard equation of parabola
- 34Paragraph: Read the following passage and answer the questions. Let be a square of side length 2 units. is the circle through vertices and i2006standard equation of parabola
- 35Match the column. Normals at are drawn to which intersect at . Then,2006Normal to Parabola
Frequently Asked Questions
1.How many questions are available for Parabola?
This chapter includes 35 questions compiled from JEE Advanced papers spanning 2006 to 2026.
2.Are these questions only from JEE Advanced, or from other exams too?
These are JEE Advanced questions specifically for the Parabola chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.
3.Is Parabola an important chapter for JEE Advanced Mathematics?
Parabola has appeared in 18 of the 21 years of JEE Advanced papers covered here, with 35 questions across 21 papers - about 2 per paper it appears in.
4.What is the difficulty level of Parabola questions in JEE Advanced?
Of the 35 questions analysed for this chapter, 20% are easy, 69% moderate and 11% tough. 2006 had the most, with 5 questions.
5.Which topics in Parabola should I focus on?
These topics have carried the most weightage in Parabola:
- Common Tangent - 7 questions (20%)
- Tangent to Parabola - 7 questions (20%)
- Normal to Parabola - 6 questions (17%)
- Common Tangent has produced the most tough questions (1).
6.Is Parabola's weightage in JEE Advanced going up or down?
Across all 21 papers analysed, Parabola has averaged about 1.7 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.