$P(6, 3)$ is a point on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ . If the normal at point $P$ intersect the $x-$ axis at $(10, 0)$ , then the eccentricity of the hyperbola is
$\sqrt {\frac{5}{3}} $
$\frac{{\sqrt {13} }}{3}$
$\sqrt {\frac{5}{2}} $
$\frac{{\sqrt {13} }}{2}$
The difference of the focal distance of any point on the hyperbola $9{x^2} - 16{y^2} = 144$, 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
If the tangents drawn to the hyperbola $4y^2 = x^2 + 1$ intersect the co-ordinate axes at the distinct points $A$ and $B$, then the locus of the mid point of $AB$ is
Locus of foot of normal drawn from any focus to variable tangent of hyperbola $4x^2-9y^2-8x- 18y = 41$ will be
The point of contact of the tangent $y = x + 2$ to the hyperbola $5{x^2} - 9{y^2} = 45$ is