The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt 2 $, is

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

A hyperbola passes through the foci of the ellipse $\frac{ x ^{2}}{25}+\frac{ y ^{2}}{16}=1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities in one, then the equation of the hyperbola is ...... .

Find the equation of axis of the given hyperbola $\frac{{{x^2}}}{3} - \frac{{{y^2}}}{2} = 1$ which is equally inclined to the axes

If the eccentricity of the standard hyperbola passing, through the point $(4, 6)$ is $2$, then the equation of the tangent to the hyperbola at $(4, 6)$ is

Let $P(6,3)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal at the point $P$ intersects the $x$-axis at $(9,0)$, then the eccentricity of the hyperbola is