If $(4, 0)$ and $(-4, 0)$ be the vertices and $(6, 0)$ and $(-6, 0)$ be the foci of a hyperbola, then its eccentricity is

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 

A hyperbola passes through the points $(3, 2)$ and $(-17, 12)$ and has its centre at origin and transverse axis is along $x$ - axis. The length of its transverse axis is

What is the slope of the tangent line drawn to the hyperbola $xy = a\,(a \ne 0)$ at the point $(a, 1)$

Length of latus rectum of hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 4\,is\,\left( {\alpha  \ne \frac{{n\pi }}{2},n \in I} \right)$

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$