The latus-rectum of the hyperbola $16x^2 - 9y^2 = 144$ is

The line $2x + y = 1$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(a > b)$. If this line passes through the point of intersection of a directrix and the positive $X$-axis,then the eccentricity of that hyperbola is

Find the coordinates of the foci and the vertices,the eccentricity,and the length of the latus rectum of the hyperbola $\frac{y^{2}}{9}-\frac{x^{2}}{27}=1$.

The equation of the hyperbola whose foci are $(6, 4)$ and $(-4, 4)$ and eccentricity $e = 2$ is given by

Find the equation of the hyperbola whose foci are $(-2, 0)$ and $(2, 0)$ and eccentricity is $2$.

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: