The equation to the chord joining two points $(x_1, y_1)$  and $(x_2, y_2)$  on the rectangular hyperbola $xy = c^2$  is

Length of latus rectum of hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} – \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 4\,is\,\left( {\alpha  \ne \frac{{n\pi }}{2},n \in I} \right)$

The locus of the point of intersection of the lines $ax\sec \theta + by\tan \theta = a$ and $ax\tan \theta + by\sec \theta = b$, where $\theta $ is the parameter, is

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

The equation of the hyperbola whose foci are the foci of the ellipse $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$ and the eccentricity is $2$, is