Question

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

Solution

Correct option is

 

The equation of chord PQ is  

      

  

Clearly, it touches the hyperbola

              .

SIMILAR QUESTIONS

Q1

The slopes of the common tangents of the hyperbolas  and 

Q2

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

Q3

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

Q4

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  

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

The product of the lengths of perpendicular drawn from any point on the hyperbola x2 – 2y2 – 2 = 0 to its asymptotes is