If Radii Of Director Circles Of  are 2r and rrespectively And ee and eh be The Eccentricities Of The Ellipse And Hyperbola Respectively, Then  

The eccentricity of the conjugate hyperbola of the hyperbola x² – 3y² = 1 is

The slopes of the common tangents of the hyperbolas  and 

A hyperbola, having the transverse axis of the length , is confocal with the ellipse 3x² + 4y² = 12. Then, its equation is  

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola x² – y² = a² is

If a hyperbola passing through the origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes, then the equations of its transverse and conjugate axes are  

If H(x, y) = 0 represents the equation of a hyperbola and A(x, y) = 0, C(x,y) = 0 the joint equation of its asymptotes and the conjugate hyperbola respectively, then for any point (α, β) in the plane,  are in

The equation of a tangent to the hyperbola  which make an angle π/4 with the transverse axis, is

For the hyperbola  which of the following remains constant with change in ‘α’

The equation of the line passing through the centre of a rectangular hyperabola is x – y – 1 = 0. If one of its asymptotes is 3x – 4y – 6 = 0, the equation of the other asymptotes is

 are two points on the hyperbola  such that  (a constant), then PQ touches the hyperbola