Locus of mid points of chords of hyperbola $x^2 -y^2 = a^2$ which are tangents to the parabola $x^2 = 4by$ will be –

The foci of a hyperbola are $( \pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2 x+3 y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the $x$ – and $y$-axes are $a$ and $b$ respectively, then $|6 a|+|5 b|$ is equal to $……….$.

The locus of the centroid of the triangle formed by any point $\mathrm{P}$ on the hyperbola $16 \mathrm{x}^{2}-9 \mathrm{y}^{2}+$ $32 x+36 y-164=0$, and its foci is:

The equation of the director circle of the hyperbola $\frac{{{x^2}}}{{16}} – \frac{{{y^2}}}{4} = 1$ is given by

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