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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?

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?

Grade:12th pass

1 Answers

ANURAG singh
11 Points
6 years ago
Let the locus of p be (h,k)So eqn. Of chord of contact to the ellipse will be xh/a^2+yk/b^2=1.Since this chord of contact is tangent to the auxillary circle,=> it`s distance from the center of the circle {I.e.(0,0)} will be the radius of the auxillary circle , I.e. `a` .Using this,|-a^2b^2|/√[(h^2)(b^4)+(k^2)(a^4)]=a=> (a^2) (b^4)=(h^2)(b^4)+(k^2)(a^4)Dividing throughout by (a^4)(b^4) and replacing h and k by x and y respectively gives us the required locus,I.e. (x^2/a^4)+(y^2/b^4)=1/(a^2)Warm regards,ANURAG class XI😊😊

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