Tangents are drawn from any point on hyperbola $4x^2 -9y^2 = 36$ to the circle $x^2 + y^2 = 9$ . If locus of midpoint of chord of contact is $\left( {\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4}} \right) = \lambda {\left( {\frac{{{x^2} + {y^2}}}{9}} \right)^2}$ , then $\lambda $ is 

The equation to the hyperbola having its eccentricity $2$ and the distance between its foci is $8$

If $\mathrm{e}_{1}$ and $\mathrm{e}_{2}$ are the eccentricities of the ellipse, $\frac{\mathrm{x}^{2}}{18}+\frac{\mathrm{y}^{2}}{4}=1$ and the hyperbola, $\frac{\mathrm{x}^{2}}{9}-\frac{\mathrm{y}^{2}}{4}=1$ respectively and $\left(\mathrm{e}_{1}, \mathrm{e}_{2}\right)$ is a point on the ellipse, $15 \mathrm{x}^{2}+3 \mathrm{y}^{2}=\mathrm{k},$ then $\mathrm{k}$ is equal to 

The eccentricity of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{{25}} = 1$ is

Find the coordinates of the foci and the vertices, the eccentricity,the length of the latus rectum of the hyperbolas : $y^{2}-16 x^{2}=16$ 

The locus of the point of intersection of the lines $bxt - ayt = ab$ and $bx + ay = abt$ is