TG EAPCET 2025 (Online) 2nd May Evening Shift | Hyperbola Question 8 | Mathematics

Let $x$ be the eccentricity of a hyperbola whose transverse axis is twice its conjugate axis. Let $y$ be the eccentricity of another hyperbola for which the distance between the focii is 3 times the distance between its directrices. Then $y^2-x^2=$

$\frac{23}{16}$

$\frac{7}{4}$

$\frac{4}{7}$

$\frac{16}{23}$

TG EAPCET 2025 (Online) 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

If the product of the perpendicular distances from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its asymptotes is $\frac{36}{13}$ and its eccentricity is $\frac{\sqrt{13}}{3}$, then $a-b=$

TG EAPCET 2024 (Online) 11th May Morning Shift

MCQ (Single Correct Answer)

-0

$P(\theta)$ is a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1, S$ is its $\mathrm{fOO}_{4 /}$ lying on the positive $X$-axis and $Q=(0,1)$. If $S Q=\sqrt{26}$ and $S P=6$, then $\theta=$

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\cos ^{-1}\left(\frac{?}{3}\right)$

TG EAPCET 2024 (Online) 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If the tangent drawn at a point $P(t)$ on the hyperbola $x^{2}-y^{2}=c^{2}$ cuts $X$-axis at $T$ and the normal drawn at the same point $P$ cuts the $Y$-axis at $N$, then the equation of the locus of the mid-point of $T N$ is

$\frac{c^{2}}{4 x^{2}}-\frac{y^{2}}{c^{2}}=1$

$\frac{x^{2}}{c^{2}}-\frac{y^{2}}{4 c^{2}}=1$

$\frac{x^{2}}{4 c^{2}}+\frac{y^{2}}{c^{2}}=1$

$x^{2}+y^{2}=4 c^{2}$

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