Question

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

Solution

Correct option is

  

,

         SS’ = 2ae

If (x, y) is center of   

  

       … (1)

 , Eccentricity of (1) is

           

                 .

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

The locus of the point of intersection of two perpendicular tangent to the ellipse , is