The equation of the normal to the curve $3x^2 - y^2 = 8$,which is parallel to the line $x + 3y = 10$,is

Find the eccentricity of a hyperbola whose latus rectum is $8$ and whose conjugate axis is half the distance between its foci.

The vertices of the hyperbola $7x^2 - 49y^2 = 343$ are

Let a line $L_{1}$ be tangent to the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{4}=1$ and let $L_{2}$ be the line passing through the origin and perpendicular to $L_{1}$. If the locus of the point of intersection of $L_{1}$ and $L_{2}$ is $(x^{2}+y^{2})^{2} = \alpha x^{2}+\beta y^{2}$,then $\alpha+\beta$ is equal to

The equation of a line passing through the centre of a rectangular hyperbola is $x - y - 1 = 0$. If one of the asymptotes is $3x - 4y - 6 = 0$,the equation of the other asymptote is:

For what value of $\gamma$ does the line $y = 2x + \gamma$ touch the hyperbola $16x^{2} - 9y^{2} = 144$?