For The Hyperbola  which Of The Following Remains Constant With Change In ‘α’

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

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

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