Question

The ,locus of the middle points of portions of the tangents to the hyperbola , intercepted between the axes is

Solution

Correct option is

4x2y2 = a2x2 – b2y2

 

Tangent at any point 

                       ….. (1)

This cuts x and y-axes at points A R (xy) be midpoint of segment AB

         .

Eliminate θ, we get locus of R. So use above equations and

⇒ 4x2y2 = a2x2 – b2y

SIMILAR QUESTIONS

Q1

If the eccentricities of the hyperbolas  and  be eand e1, then 

Q2

 

The locus rectum of the hyperbola

9x2 – 16y2 – 18x – 32y – 151 = 0 is

Q3

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

Q4

The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is

Q5

If the polar of a point with respect to  toches the hyperbola , then the locus of the point is

Q6

The locus of pole of any tangent to the circle x2 + y2 = 4 w.r.t. the hyperbola x2 – y= 4 is the circle

Q7

The foci of a hyperbola coincide with the foci of the ellipse . The equation of the hyperbola if its eccentricity is 2, is

Q8

The normal to the rectangular hyperbola xy = c2 at the point ‘t’ meets the curve again at point “t” such that

Q9

PN is the ordinate of any point P on the hyperbola  and AA’ is its transverse axis. If Q divides AP in the ratio a2 : b2, then NQ is