The length of the conjugate axis of a hyperbola is greater than the length of the transverse axis. Then, the eccentricity $e$ is

The equation of a tangent to the hyperbola $5x^{2}-y^{2}=5$ which passes through the external point $(2, 8)$ is:

The lines of the form $x \cos \phi + y \sin \phi = P$ are chords of the hyperbola $4x^2 - y^2 = 4a^2$ which subtend a right angle at the centre of the hyperbola. If these chords touch a circle with centre at $(0,0)$,then the radius of that circle is

If $5x + 9 = 0$ is the directrix of the hyperbola $16x^2 - 9y^2 = 144,$ then its corresponding focus is

The area of the triangle formed by the tangent to the hyperbola $xy = a^2$ and the coordinate axes is:

If the equation of a hyperbola is $9x^2 - 16y^2 + 72x - 32y - 16 = 0$,then the equation of its conjugate hyperbola is