Hyperbola

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

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

If the product of the lengths of the perpendiculars from any point on the hyperbola $16 x^2-25 y^2=400$ to its asymptotes is $p$ and the angle between the two asymptotes is $\theta$, then $p \tan \frac{\theta}{2}=$

If $e_1, e_2$ are respectively the eccentricities of the curves $9 x^2-16 y^2-144=0$ and $9 x^2-16 y^2+144=0$, then $\frac{e_1^2 e_2^2}{e_1^2+e_2^2}=$

From any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, tangents are drawn to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=2$. The area of the figure formed by the chord of contact of that point and the…

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

If the focal chord of the hyperbola subtends a right angle at the center, then its eccentricity is

If the equation of one asymptote of the hyperbola $14 x^2+38 x y+20 y^2+x-7 y-91=0$ is $7 x+5 y-3=0$, then the other asymptote 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 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 6 and eccentricity of the hyperbola is $\sqrt{3}$, then the length of the conjugate…

If a circle of radius 4 cm passes through the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is