Hyperbola

If the latusrectum of a hyperbola subtends a right angle at the other focus, then its eccentricity is

Let the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$be $\frac{5}{4}$. If the equation of the normal at the point $\left(\frac{8}{\sqrt{5}},\frac{12}{5}\right)$on the hyperbola is…

Let the eccentricity of an ellipse$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$is reciprocal to that of the hyperbola $2x^{2}-2y^{2}=1$. If the ellipse intersects the hyperbola at right angles, then square of length of…

The eccentricity of the hyperbola $16 x^2-9 y^2=1$ is

The foci of the hyperbola $4 x^2-9 y^2-1=0$ are

The angle between the asymptotes of the hyperbola $x^2-3 y^2=3$ is

If the latus rectum subtends a right angle at center of the hyperbola, then its eccentricity is

A chord through the point $(1,-2)$ cuts the curve $3 x^2-y^2-2 x+4 y=0$ at $P$ and $Q$. If $P Q$ subtends an angle $\theta$ at the origin, then $\theta$ equals

If the transverse and conjugate axes of hyperbola are equal, then its eccentricity is

If the equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola then

If the latus rectum of a hyperbola through one focus subtends an angle $\(60^{\circ}\)$ at the other focus, then its eccentricity is

Let the points $\mathrm{P}_1\left(\frac{\pi}{4}\right), \mathrm{P}_2\left(\frac{3 \pi}{4}\right), \mathrm{P}_3\left(\frac{5 \pi}{4}\right)$ and $\mathrm{P}_4\left(\frac{7 \pi}{4}\right)$ given in parametric form, lie on…