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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

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

Grade:11

3 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Please write the Question in a standard form or attach an image of the question

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Vikas TU
14149 Points
4 years ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
Arun
25750 Points
4 years ago
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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