Question

The locus of the poles of the tangents to the ellipse  w.r.t. the circle x2 + y2 = a2 is

Solution

Correct option is

Ellipse

A tangent to ellipse is

                                             … (1)

Let (x1y1) be pole of tangent w.r.t. circle

         x2 + y2 = a2                 xx+ yy1 = a2        … (2)

(1) and (2) are same.

Now a compare and find locus of  (x1y1).

SIMILAR QUESTIONS

Q1

If CP and CD is a pair of semi-conjugate diameters of the ellipse,

, then CP2 + CD2 =

Q2

The line y = 2t2 meets the ellipse  in real point if

Q3

The locus of the foot of the perpendiculars to any tangent of an ellipse from the foci is

Q4

The product of the perpendiculars from the foci upon any tangent to the ellipse  is

Q5

If P and D are the extremities of a pair of conjugate diameters of the ellipse , then the locus of the middle point ofPD is

Q6

The equation of the ellipse, referred to its axes as the axes of coordinates, which passes through the points (2, 2) and (1, 4) is

Q7

If CP and CD be any two semi-conjugate diameters of the ellipse  and the circle with CP and CD as diameters intersect in R, then R lies on the curve

Q8

The locus of the point whose polar with respect to the ellipse  touches the parabola y2 = 4kx is 

Q9

The polar of lx + my =1 with respect to the ellipse  lies on the ellipse  if

Q10

A variable point P on the ellipse eccentricity e is joined to its foci S, S’. The locus of the incentre of   is an ellipse of eccentricity