Two concentric hyperbolas, whose axes meet at angle of `45^@`, cut

9.(i) Two tangents to a parabola y24ax meet at an angle of 45. Prove that the locus of their point of th guadrilntoral whose vortices lie at the pints of intersection of the parabola intersection is the curve y 2-4ax=(x+a)2

Find the equation of the hyperbola, whose axes are axes of coordinates and lengths of transverse and conjugate axes are 5 and 6 respectively

The differential equation of rectangular hyperbolas whose axes are asymptotes of the hyperbola x^2 - y^2= a^2 , is :

The differential equation of rectangular hyperbolas whose axes are asymptotes of the hyperbola x^2 - y^2= a^2 , is :

Find the equation of the hyperbola, whose axes are axes of coordinates and lengths of conjugate axis and latus rectum are 2 (8)/(3) respectively.

The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola,is

The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola, is

Find the equation of the hyperbola whose axes are the axes of coordinates and length of conjugate axis is 5 and the distance between the foci is 13.

Find the equation of the hyperbola, whose axes are axes of coordinates and eccentricity is (sqrt(13))/(3) and the sum of the squares of the lengths of axes is 52.