A hyperbola passes through the focus of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1,$ and its transverses and conjugate axes coincide with the major and minor axes of the ellipse. If the product of the eccentricites of the two curve is $1$, then the focus of the hyperbola is

If $\frac { (3x-4y-{ 1) }^{ 2 } }{ 100 } -\frac { (4x+3y-{ 1) }^{ 2 } }{ 225 } =1,$ then length latusrectum of hyperbola is-

The hyperbola $\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } -\dfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$ passes through the point of intersection of the lines $x-3\sqrt { 5 } y=0$ and $\sqrt { 5 } x-2y=13$ and the length of its flatus rectum is 4/3 units. The coordinates of its focus are-

If the latus rectum subtends a right angel at the center of a hyperbola, then its eccentricity is 

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