With one focus of the hyperbola $\frac{{{x^2}}}{9}\,\, - \,\,\frac{{{y^2}}}{{16}}\,\, = \,\,1$ as the centre , a circle is drawn which is tangent to the hyperbola with no part of the circle being outside the hyperbola. The radius of the circle is
$less\ than$ $2$
$2$
$\frac{{11}}{3}$
$none$
A hyperbola passes through the point $P\left( {\sqrt 2 ,\sqrt 3 } \right)$ has foci at $\left( { \pm 2,0} \right)$. Then the tangent to this hyperbola at $P$ also passes through the point
The eccentricity of the conjugate hyperbola of the hyperbola ${x^2} - 3{y^2} = 1$, is
The locus of middle points of the chords of the circle $x^2 + y^2 = a^2$ which touch the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is
The product of the perpendiculars drawn from any point on a hyperbola to its asymptotes is
Latus rectum of the conic satisfying the differential equation, $ x dy + y dx = 0$ and passing through the point $ (2, 8) $ is :