Conic Sections

JEE Advanced · Mathematics · 71 past questions

11 of 71 · show all

1. Q15 2022 Paper 2

   Consider the hyperbola…

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2. 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…

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3. 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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4. 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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5. 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…

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6. Q46 2012 Paper 1

   Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1$.…

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7. 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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8. 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 $P$…

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9. 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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10. Q66 2008 Paper 2

    Consider a branch of the hyperbola…

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11. Q67 2007 Paper 1

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

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