Question

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

Solution

Correct option is

2(x2 + y2)2 = a2x2 + b2y2

C(0,0), 

Equation of the circle with CP as diameter,

             (x – x1)(x – x2) + (y – y1)(y – y2) = 0

                            … (1)

Similarly equation of circle with CD as diameter CD is 

                               … (2)

Locus of point of int of (1) and (2) is obtained by elimination θ.

SIMILAR QUESTIONS

Q1

The area of the parallelogram formed by tangents at the extremities of two conjugate diameters of the ellipse  is equal to

Q2

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse  is 900 then the eccentricity is

Q3

The tangent and the normal to the ellipse x2 + 4y2 = 4 at a point P on it meet the major axis in Q and R respectively. If QR = 2, then the eccentric angle of P is

Q4

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

, then CP2 + CD2 =

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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