AP EAPCET 2024 - 22th May Morning Shift | Hyperbola Question 6 | Mathematics

If the ellipse $4 x^2+9 y^2=36$ is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hyperbola lie on the circle

$x^2+y^2=81$

$x^2+y^2=16$

$x^2+y^2=25$

$x^2+y^2=5$

AP EAPCET 2024 - 22th May Morning Shift

MCQ (Single Correct Answer)

-0

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)

-0

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

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