$A$ point on the curve $\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1$ is

If the circle $x^2 + y^2 = a^2$ intersects the hyperbola $xy = c^2$ in four points $P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4)$,then:

Find the length of the latus rectum of the hyperbola $16x^2 - 9y^2 = 144$. (in $/3$)

The equation of a tangent to the hyperbola $4x^2 - 5y^2 = 20$ parallel to the line $x - y = 2$ is

If the eccentricities of the hyperbolas $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and $\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1$ are $e$ and $e_1$ respectively,then $\frac{1}{e^2} + \frac{1}{e_1^2} = $

If 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 the major and minor axes of the ellipse respectively,and the product of their eccentricities is $1$,then: