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Conic Sections

JEE Advanced · Mathematics · 71 past questions

  1. Q1 2026 Paper 1
    Let $P$ be the point on the parabola $y=x^2$ such that the slope of the tangent to the parabola at the point…
  2. Q2 2026 Paper 2
    Let $T$ be the tangent to the parabola $y^2=16x$ at the point $(64, 32)$. Let $L$ be the tangent to the same…
  3. Q3 2026 Paper 2
    Consider the ellipse $E$ given by $\frac{x^2}{18}+\frac{y^2}{12}=1$. Let $H$ be the hyperbola whose…
  4. Q4 2026 Paper 2
    Question Stem for Question Nos. 17 and 18…
  5. Q5 2026 Paper 2
    Question Stem for Question Nos. 17 and 18…
  6. Q6 2025 Paper 2
    Let $S$ denote the locus of the point of intersection of the pair of lines…
  7. Q7 2025 Paper 2
    Let $S$ denote the locus of the mid-points of those chords of the parabola $y^2 = x$, such that the area of…
  8. Q8 2024 Paper 1
    Consider the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let $S(p,q)$ be a point in the first quadrant such that…
  9. Q9 2024 Paper 2
    Let $A_1, B_1, C_1$ be three points in the $xy$-plane. Suppose that the lines $A_1C_1$ and $B_1C_1$ are…
  10. Q10 2024 Paper 2
    A normal with slope $\frac{1}{\sqrt6}$ is drawn from the point $(0,-\alpha)$ to the parabola $x^2=-4ay$…
  11. Q11 2023 Paper 1
    Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E:\dfrac{x^2}{6}+\dfrac{y^2}{3}=1$ and…
  12. Q12 2023 Paper 1
    Let $P$ be a point on the parabola $y^2=4ax$, where $a>0$. The normal to the parabola at $P$ meets the…
  13. Q13 2022 Paper 1
    Consider the parabola $y^2 = 4x$. Let $S$ be the focus of the parabola. A pair of tangents drawn to the…
  14. Q14 2022 Paper 1
    Consider the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$.…
  15. Q15 2022 Paper 2
    Consider the hyperbola…
  16. Q16 2021 Paper 1
    Consider the lines $L_1$ and $L_2$ defined by…
  17. Q17 2021 Paper 1
    Consider the lines $L_1$ and $L_2$ defined by…
  18. Q18 2021 Paper 2
    Let $E$ denote the parabola $y^2 = 8x$. Let $P = (-2, 4)$, and let $Q$ and $Q'$ be two distinct points on $E$…
  19. Q19 2021 Paper 2
    Let $E$ be the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$. For any three distinct points $P, Q$ and $Q'$ on…
  20. Q20 2020 Paper 1
    Let $a, b$ and $\lambda$ be positive real numbers. Suppose $P$ is an end point of the latus rectum of the…
  21. Q21 2020 Paper 2
    Let $a$ and $b$ be positive real numbers such that $a>1$ and $b<a$. Let $P$ be a point in the first quadrant…
  22. Q22 2019 Paper 1
    Define the collections $\{E_1, E_2, E_3, ...\}$ of ellipses and $\{R_1, R_2, R_3, ...\}$ of rectangles as…
  23. Q23 2018 Paper 2
    Consider two straight lines, each of which is tangent to both the circle $x^2+y^2=\frac{1}{2}$ and the…
  24. Q24 2018 Paper 2
    Let $H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a>b>0$, be a hyperbola in the $xy$-plane whose conjugate…
  25. Q25 2017 Paper 1
    If $2x - y + 1 = 0$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{16} = 1$, then which of the…
  26. Q26 2017 Paper 1
    If a chord, which is not a tangent, of the parabola $y^2 = 16x$ has the equation $2x + y = p$, and midpoint…
  27. Q27 2017 Paper 1
    Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the…
  28. Q28 2017 Paper 1
    Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the…
  29. Q29 2017 Paper 1
    Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the…
  30. Q30 2016 Paper 2
    Let $P$ be the point on the parabola $y^2=4x$ which is at the shortest distance from the center $S$ of the…
  31. Q31 2016 Paper 2
    PARAGRAPH 2…
  32. Q32 2016 Paper 2
    PARAGRAPH 2…
  33. Q33 2015 Paper 1
    Let the curve $C$ be the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $A$ and…
  34. Q34 2015 Paper 1
    Let $P$ and $Q$ be distinct points on the parabola $y^2=2x$ such that a circle with $PQ$ as diameter passes…
  35. Q35 2015 Paper 2
    Suppose that the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ are $(f_1, 0)$ and $(f_2, 0)$ where…
  36. Q36 2015 Paper 2
    Let $E_1$ and $E_2$ be two ellipses whose centers are at the origin. The major axes of $E_1$ and $E_2$ lie…
  37. Q37 2015 Paper 2
    Consider the hyperbola $H: x^2-y^2=1$ and a circle $S$ with center $N(x_2,0)$. Suppose that $H$ and $S$ touch…
  38. Q38 2014 Paper 2
    Let $a, r, s, t$ be nonzero real numbers. Let $P(at^2, 2at)$, $Q$, $R(ar^2, 2ar)$ and $S(as^2, 2as)$ be…
  39. Q39 2014 Paper 2
    Let $a, r, s, t$ be nonzero real numbers. Let $P(at^2, 2at)$, $Q$, $R(ar^2, 2ar)$ and $S(as^2, 2as)$ be…
  40. Q40 2014 Paper 2
    Choices for the correct combination of elements from List-I and List-II are given as options (A), (B), (C)…
  41. Q41 2013 Paper 1
    A vertical line passing through the point $(h, 0)$ intersects the ellipse $\dfrac{x^2}{4}+\dfrac{y^2}{3}=1$…
  42. Q42 2013 Paper 2
    Paragraph for Questions 55 and 56…
  43. Q43 2013 Paper 2
    Paragraph for Questions 55 and 56…
  44. Q44 2013 Paper 2
    A line $L: y = mx + 3$ meets $y$-axis at $E(0, 3)$ and the arc of the parabola $y^2 = 16x$, $0 \le y \le 6$…
  45. Q45 2012 Paper 1
    The ellipse $E_1:\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to…
  46. Q46 2012 Paper 1
    Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1$.…
  47. Q47 2011 Paper 1
    Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the…
  48. Q48 2011 Paper 1
    Consider the parabola $y^2 = 8x$. Let $\Delta_1$ be the area of the triangle formed by the end points of its…
  49. Q49 2011 Paper 2
    Let $P(6,3)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal at the point $P$…
  50. Q50 2011 Paper 2
    Let $(x,y)$ be any point on the parabola $y^2=4x$. Let $P$ be the point that divides the line segment from…
  51. Q51 2011 Paper 2
    Let $L$ be a normal to the parabola $y^2=4x$. If $L$ passes through the point $(9,6)$, then $L$ is given by
  52. Q52 2010 Paper 1
    Let A and B be two distinct points on the parabola $y^2 = 4x$. If the axis of the parabola touches a circle…
  53. Q53 2010 Paper 1
    Paragraph for Questions 45 to 46…
  54. Q54 2010 Paper 1
    Paragraph for Questions 45 to 46…
  55. Q55 2010 Paper 1
    The line $2x+y=1$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this line passes…
  56. Q56 2010 Paper 2
    Paragraph for Questions 34 to 36.…
  57. Q57 2010 Paper 2
    Paragraph for Questions 34 to 36.…
  58. Q58 2009 Paper 1
    The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the…
  59. Q59 2009 Paper 1
    Match the conics in Column I with the statements/expressions in Column II.
  60. Q60 2009 Paper 2
    The normal at a point $P$ on the ellipse $x^2+4y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid point of…
  61. Q61 2009 Paper 2
    An ellipse intersects the hyperbola $2x^2 - 2y^2 = 1$ orthogonally. The eccentricity of the ellipse is…
  62. Q62 2009 Paper 2
    The tangent $PT$ and the normal $PN$ to the parabola $y^2 = 4ax$ at a point $P$ on it meet its axis at points…
  63. Q63 2008 Paper 1
    Consider the two curves…
  64. Q64 2008 Paper 1
    Let $a$ and $b$ be non-zero real numbers. Then, the equation…
  65. Q65 2008 Paper 1
    Let $P(x_1, y_1)$ and $Q(x_2, y_2)$, $y_1 < 0$, $y_2 < 0$, be the end points of the latus rectum of the…
  66. Q66 2008 Paper 2
    Consider a branch of the hyperbola…
  67. Q67 2007 Paper 1
    A hyperbola, having the transverse axis of length $2\sin\theta$, is confocal with the ellipse…
  68. Q68 2007 Paper 1
    M61-63: Paragraph for Question Nos. 61 to 63…
  69. Q69 2007 Paper 1
    M61-63: Paragraph for Question Nos. 61 to 63…
  70. Q70 2007 Paper 1
    M61-63: Paragraph for Question Nos. 61 to 63…
  71. Q71 2007 Paper 2
    STATEMENT-1: The curve $y = \dfrac{-x^2}{2} + x + 1$ is symmetric with respect to the line $x = 1$.…