Question

If tangent to any members of family of hyperbolas  is not a normal to any member of family of circles , where μ is any real parameter, then θbelongs to  

Solution

Correct option is

All of these

 

The equation of the hyperbola is xy = c2, where . The equation of any tangent to it is . If it is normal to each member of the family of circles, it must pass through the centre of each circle i.e. (1, 1). 

This will have non-real roots, if  

       

.

SIMILAR QUESTIONS

Q1

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  

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

The foci of a hyperbola are (–5, 18) and (10, 20) and it touches the y-axis. The length of its transverse axis is