Find the locus of point of intersection ...

Find the locus of point of intersection of tangents to the ellipse `x^2/a^2+y^2/b^2=1` which are inclined at an angle `alpha` with each other.

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The correct Answer is:

`|x^(2)+y^(2)-(a^(2)+b^(2))|^(2) tan^(2) alpha=4(b^(2)x^(2)+a^(2)y^(2)-a^(2)b^(2))`

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