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HYPERBOLA

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2023
Let $H_n=\frac{x^2}{1+n}-\frac{y^2}{3+n}=1, n \in N$. Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_k$ is a rational number. If...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $A$ be a square matrix of order 2 such that $|A|=2$ and the sum of its diagonal elements is -3. If the points (...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $\mathrm{H}: \frac{-\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1$ be the hyperbola, whose eccentricity is $\sqrt{3}$ and the length of the latus rectum is $4 \sqrt{3}$. Suppose the point $...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let the latus rectum of the hyperbola x^2/9-y^2/b^2 =1 subtend an angle of π/3 at the centre of the hyperbola. If b^2 is equal to...
JEE Main Mathematics Medium
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Q JEE-Main 2024
Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ be an ellipse, whose eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latus rectum is $\sqrt{14}$. Then the square of the eccentricity...
JEE Main Mathematics Easy
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Q JEE-Main 2024
For $0<\theta<\pi / 2$, if the eccentricity of the hyperbola $x^2-y^2 \operatorname{cosec}^2 \theta=5$ is $\sqrt{7}$ times eccentricity of the ellipse $x^2 \operatorname{cosec}^2 \theta+y^2=5$, then the...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If the foci of a hyperbola are same as that of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ and the eccentricity of the hyperbola is $\frac{15}{8}$ times the eccentricity...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Consider the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ having one of its focus at ${\rm{P}}( - 3,0)$. If the latus ractum through its other focus...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If A and B are the points of intersection of the circle $x^{2}+y^{2}-8 x=0$ and the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ and a point $P$ moves on the...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let the product of the focal distances of the point $P(4,2\sqrt 3)$ on the hyperbola ${\rm{H}}:\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ be 32. Let the length...
JEE Main Mathematics Medium
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