Question

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

Solution

Correct option is

 

R(h, k) is meddle of PQ . 

        

            

Locus of (h, k) is .

SIMILAR QUESTIONS

Q1

If the polar with respect to the parabola y2 = 4ax touches the ellipse , then the locus of its pole is  

Q2

The locus of mid-point of the portions of the tangents to the ellipse  included between the axes is the curve 

Q3

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

Q4

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

Q5

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

Q6

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

, then CP2 + CD2 =

Q7

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

Q8

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

Q9

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

Q10

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