AP EAPCET 2024 - 22th May Morning Shift | Hyperbola Question 7 | Mathematics

If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\sec \alpha$, then area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is

$a^2 b^2 \sec ^2 \alpha$

$\frac{b^2}{|\tan \alpha|}$

$a^2 \tan ^2 \alpha$

$\left(a^2+b^2\right) \tan ^2 \alpha$

AP EAPCET 2024 - 22th May Morning Shift

MCQ (Single Correct Answer)

-0

If $e_1$ and $e_2$ are respectively the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conjugate hyperbola, then the line $\frac{x}{2 e_1}+\frac{y}{2 e_2}=1$ touches the circle having centre at the origin, then its radius is

$e_1+e_2$

$e_1 e_2$

AP EAPCET 2024 - 21th May Evening Shift

MCQ (Single Correct Answer)

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The descending order of magnitude of the eccentricities of the following hyperbolas is A. A hyperbola whose distance between foci is three times the distance between its directrices. B. Hyperbola in which the transverse axis is twice the conjugate axis. C. Hyperbola with asymptotes $x+y+1=0, x-y+3=0$

$C, A, B$

B, C, A

C, B, A

A, C, B

AP EAPCET 2024 - 21th May Morning Shift

MCQ (Single Correct Answer)

-0

The equation of the pair of asymptotes of the hyperbola $4 x^2-9 y^2-24 x-36 y-36=0$ is

$2 x^2-x y-3 y^2-14 x-9 y-12=0$

$2 x^2-x y-3 y^2-2 x+3 y=0$

$2 x^2-5 x y+3 y^2-22 x+27 y+60=0$

$4 x^2-9 y^2-24 x-36 y=0$

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