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Any tangent to an ellips (x^(2))/(a^(2))...

Any tangent to an ellips `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, (a gt b)` cut by the tangents at the end points of major axis is T and T' . Prove that the length of intercept of the major axis cut by the circle describe on T T' as diameter is constant and equal to `2sqrt(a^(2)-b^(2))`.

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