A hyperbola whose transverse axis is along the major axis of then conic, $\frac{{{x^2}}}{3} + \frac{{{y^2}}}{4} = 4$ and has vertices at the foci of this conic . If the eccentricity of the hyperbola is $\frac{3}{2}$ , then which of the following points does $NOT$ lie on it ?

Consider a branch of the hyperbola $x^2-2 y^2-2 \sqrt{2} x-4 \sqrt{2} y-6=0$ with vertex at the point $A$. Let $B$ be one of the end points of its latus rectum. If $\mathrm{C}$ is the focus of the hyperbola nearest to the point $\mathrm{A}$, then the area of the triangle $\mathrm{ABC}$ is

Find the equation of the hyperbola satisfying the give conditions: Vertices $(0,\,\pm 5),$ foci $(0,\,±8)$

If $e$ and $e’$ are the eccentricities of the ellipse $5{x^2} + 9{y^2} = 45$ and the hyperbola $5{x^2} - 4{y^2} = 45$ respectively, then $ee' = $

The equation of a line passing through the centre of a rectangular hyperbola is $x -y -1 = 0$. If one of the asymptotes is $3x -4y -6 = 0$, the equation of other asymptote 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