The Product Of The Lengths Of Perpendicular Drawn From Any Point On The Hyperbola x2 – 2y2 – 2 = 0 To Its Asymptotes Is

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

If radii of director circles of  are 2r and rrespectively and e_e and e_h be the eccentricities of the ellipse and hyperbola respectively, then  

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

The foci of a hyperbola are (–5, 18) and (10, 20) and it touches the y-axis. The length of its transverse axis is