Conic Sections

JEE Advanced · Mathematics · 71 past questions

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1. 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…

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2. 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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3. 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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4. 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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5. 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…

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6. 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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7. 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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8. 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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9. 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

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10. 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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