Question

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

Solution

Correct option is

a2l2 + b2m2 = 4

Let (x1y1) be pole of lx + my =1        … (1)

w.r.t. ellipse                   … (2)

                                  … (3)

Compare (1) and (2)      x1 = a2l,  y1 = b2m

Now (x1y1) lie on

       

   a2l2 + b2m2 = 4.

SIMILAR QUESTIONS

Q1

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

Q2

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

, then CP2 + CD2 =

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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