The point of contact of the line $y = x - 1$ with the hyperbola $3x^2 - 4y^2 = 12$ is

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

If $\frac{x^{2}}{36}-\frac{y^{2}}{k^{2}}=1$ is a hyperbola,then which of the following statements can be true?

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

The length of the transverse axis of a hyperbola is $7$ and it passes through the point $(5, -2)$. The equation of the hyperbola is

The line segment joining the foci of the hyperbola $x^{2}-y^{2}+1=0$ is one of the diameters of a circle. The equation of the circle is