AP EAPCET 2024 - 19th May Evening Shift | Hyperbola Question 17 | Mathematics

If the product of eccentricities of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=-1$ is 1 , then $b^2=$

$\frac{12}{25}$

144

$\frac{144}{25}$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

-0

If the line $5 x-2 y-6=0$ is a tangent to the hyperbola $5 x^2-k y^2=12$, then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)(p<0)$ is

$\sqrt{6} x+2 y=0$

$2 \sqrt{6} x+3 y=3$

$\sqrt{6} x-5 y=21$

$3 \sqrt{6} x-y=21$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

-0

If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity, then the pole of the line $x+y-1=0$ with respect to this hyperbola is

$\left(k, \frac{\sqrt{30}}{2}\right)$

$\left(-k, \frac{\sqrt{3} e}{2}\right)$

$\left(-k,-\frac{\sqrt{3} e}{2}\right)$

$\left(k_1-\frac{\sqrt{3} e}{2}\right)$

AP EAPCET 2022 - 5th July Morning Shift

MCQ (Single Correct Answer)

-0

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola $$x^2-y^2=a^2$$ is

$$y^4-x^4=4 a^2 x^2 y^2$$

$$y^2-x^2=4 a^2 x^2 y^2$$

$$a^2\left(y^2-x^2\right)=4 x^2 y^2$$

$$y^2+x^2=4 a^2 x^2 y^2$$

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