From a point p tangents are drawn to the ellipse x^2÷a^2+y^2÷b^2=1.if the chord of contact touches the ellipse x^2÷a^2+y^2÷b^2=1.then find the locus of p

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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)