Question

From a point p tangents are drawn to the ellipse .if the chord of contact touches the ellipse

Answer 1

The question seems to be incomplete. Here is the complete question:

From a point P tangents are drawn to the ellipse  x2/a2 +y2/b2 = 1 . if the chord of contact touches the ellipse the auxiliary circle, then locus of P is?

Answer

Let the locus of p be (h,k)

The equation of chord of contact to the ellipse will be eqaut to:

xh/a^2+yk/b^2=1.

The distance from the center of the circle {I.e.(0,0)} will be the radius of the auxiliary circle.

-a^2b^2|/√[(h^2)(b^4)+(k^2)(a^4)]=a=> (a^2) (b^4)=(h^2)(b^4)+(k^2)(a^4)

We finally get this as our answer: (x^2/a^4)+(y^2/b^4)=1/(a^2)

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