Conic Sections

JEE Advanced · Mathematics · 71 past questions

47 of 71 · show all

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…

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2. 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…

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3. Q4 2026 Paper 2

   Question Stem for Question Nos. 17 and 18…

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4. Q6 2025 Paper 2

   Let $S$ denote the locus of the point of intersection of the pair of lines…

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5. 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…

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6. 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…

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7. Q10 2024 Paper 2

   A normal with slope $\frac{1}{\sqrt6}$ is drawn from the point $(0,-\alpha)$ to the parabola $x^2=-4ay$…

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8. 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…

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9. Q14 2022 Paper 1

   Consider the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$.…

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10. Q16 2021 Paper 1

    Consider the lines $L_1$ and $L_2$ defined by…

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11. 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 $E$…

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12. 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…

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13. 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…

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14. 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…

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15. 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…

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16. 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…

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17. 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…

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18. Q27 2017 Paper 1

    Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the…

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19. Q28 2017 Paper 1

    Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the…

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20. Q29 2017 Paper 1

    Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the…

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21. 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…

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22. Q31 2016 Paper 2

    PARAGRAPH 2…

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23. 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…

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24. 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…

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25. 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…

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26. 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…

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27. 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…

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28. Q40 2014 Paper 2

    Choices for the correct combination of elements from List-I and List-II are given as options (A), (B), (C)…

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29. Q42 2013 Paper 2

    Paragraph for Questions 55 and 56…

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30. Q43 2013 Paper 2

    Paragraph for Questions 55 and 56…

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31. 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…

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32. 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…

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33. Q53 2010 Paper 1

    Paragraph for Questions 45 to 46…

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34. 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…

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35. Q57 2010 Paper 2

    Paragraph for Questions 34 to 36.…

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36. Q58 2009 Paper 1

    The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the…

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37. Q59 2009 Paper 1

    Match the conics in Column I with the statements/expressions in Column II.

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38. 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…

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39. Q61 2009 Paper 2

    An ellipse intersects the hyperbola $2x^2 - 2y^2 = 1$ orthogonally. The eccentricity of the ellipse is…

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40. 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…

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41. Q63 2008 Paper 1

    Consider the two curves…

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42. 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…

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43. Q66 2008 Paper 2

    Consider a branch of the hyperbola…

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44. Q67 2007 Paper 1

    A hyperbola, having the transverse axis of length $2\sin\theta$, is confocal with the ellipse…

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45. Q68 2007 Paper 1

    M61-63: Paragraph for Question Nos. 61 to 63…

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46. Q69 2007 Paper 1

    M61-63: Paragraph for Question Nos. 61 to 63…

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47. Q70 2007 Paper 1

    M61-63: Paragraph for Question Nos. 61 to 63…

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