The Equation Of A Tangent To The Hyperbola  which Make An Angle π/4 With The Transverse Axis, Is

If x = 9 is the chord of contact of the hyperbola x² – y² = 9, then the equation of the corresponding pair of tangents is

If e and e’ be the eccentricities of two conics S = 0 and S’ = 0 and if e² +e’² = 3, then both S and S’ can be  

If e₁ is the eccentricity of the ellipse  and e₂ is the eccentricity of the hyperbola passing through the foci of the ellipse and e₁e₂ = 1, then the equation of the parabola, is 

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

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