Hyperbola Test ...

The eccentricity of the hyperbola 4x²–9y²–8x = 32 is

The locus of the point of intersection of the lines √3x - y - 4√3k = 0 and √3kx + ky - 4√3 = 0 for different values of k is

If the latus rectum of an hyperbola be 8 and eccentricity be 3/√5 then the equation of the hyperbola is

If the centre, vertex and focus of a hyperbola be (0, 0), (4, 0) and (6, 0) respectively, then the equation of the hyperbola is

The equation of the hyperbola whose foci are (6, 5), (–4, 5) and eccentricity 5/4 is

The vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foci is at (18, 0). The equation of the hyperbola is

The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is

If the eccentricity of the hyperbola x² – y² sec² a = 5 is (√3) times the eccentricity of the ellipse x² sec² a + y² = 25, then a value e of a is

AB is a double ordinate of the hyperbola  such that DAOB (where `O' is the origin) is an equilateral triangle, then the eccentricity e of the hyperbola satisfies

The equation of the tangent lines to the hyperbola x² – 2y² = 18 which are perpendicular to the line y = x are