If the latus rectum of a hyperbola subtends an angle of $120^{\circ}$ at its centre,then its eccentricity is

The normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1$ at the point $(8, 3\sqrt{3})$ on it passes through the point

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 asymptotes is

The eccentricity of the hyperbola $25x^2 - 9y^2 = 225$ is...

Let $A(\sec \theta, 2 \tan \theta)$ and $B(\sec \phi, 2 \tan \phi)$,where $\theta+\phi=\pi/2$,be two points on the hyperbola $2x^2-y^2=2$. If $(\alpha, \beta)$ is the point of intersection of the normals to the hyperbola at $A$ and $B$,then $(2\beta)^2$ is equal to ..... .

The line $2x + \sqrt{6}y = 2$ is a tangent to the curve $x^2 - 2y^2 = 4$. The point of contact is