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

Let  be two points on the hyperbola . If (h, k) is the point of intersection of the normal of P and Q, then k is equal to

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  

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