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The tangent at a point P(acos theta,bsin...

The tangent at a point `P(acos theta,bsin theta)` on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:

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