The Polar Of lx + My =1 With Respect To The Ellipse  lies On The Ellipse  if

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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

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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

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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