Question

If H(xy) = 0 represents the equation of a hyperbola and A(xy) = 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

Solution

Correct option is

A.P.

 

Let, 

      

     

We observe that  

      

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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 

Q5

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

Q6

The slopes of the common tangents of the hyperbolas  and 

Q7

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

Q8

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

Q9

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  

Q10

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