The eccentricity of the hyperbola $4x^2 - 9y^2 = 16$ is

Tangents are drawn to the hyperbola $x^2 - 9y^2 = 9$ from the point $(3, 2)$. The area of the triangle formed by the tangents and the chord of contact is . . . . . . sq units.

If the line $ax + by = 1$ is normal to the hyperbola $\frac{x^2}{p^2} - \frac{y^2}{q^2} = 1$,then $\frac{p^2}{a^2} - \frac{q^2}{b^2}$ is equal to (where $a, b, p, q \in R^+$):

Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $H$ is $\alpha$ and the length of its conjugate axis is $\beta$,then $3 \alpha^2+2 \beta^2$ is equal to :

Find the eccentricity of the hyperbola $16x^{2} - 32x - 3y^{2} + 12y = 44$.

The eccentricity of a rectangular hyperbola is