Let a and b respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation `9e^2 - 18e + 5 = 0`. If `S(5,0)` is a focus and `5x = 9` is the corresponding directrix of this hyperbola, then `a^2 - b^2` is equal to

A conic has focus (1,0) and corresponding directrix x+y=5. If the eccentricity of the conic is 2, then its equation is

Find the length of the transverse and conjugate axes, eccentricity, centre, foci and directrices of the hyperbola . 9x^2 - 16y^2 - 72x + 96y - 144 = 0

if 5x+9=0 is the directrix of the hyperbola 16x^(2)-9y^(2)=144, then its corresponding focus is

If 5x +9 =0 is the directtrix of the hyperbola 16x^(2) -9y^(2)=144, then its corresponding focus is

Find the equation of the hyperbola whose focus is (1,1), eccentricity is 2 and equation of directrix is x+y+1=0.

Find the equation of the hyperbola whose one focus is (-1, 1) , eccentricity = 3 and the equation of the corresponding directrix is x - y + 3 = 0 .

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. If l and l\' be the length of semi latera recta of ellipse and hyperbola, then ll\'= (A) 144/15 (B) 256/15 (C) 225/12 (D) none of these