# Eccentricity Of A Ellipse

Geometry Level 3

If the tangent at any point of an ellipse $$\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\quad ,\quad a\quad >\quad b$$ makes an angle $$\alpha =\frac { 5\pi }{ 6 }$$ with the major axis and angle $$\beta =\frac { \pi }{ 3 }$$ with the focal radius of the point of contact then find the eccentricity 'e' of the ellipse$$\\$$

S is the focus of the ellipse,$$\\$$ PT is the tangent with P as the point of contact,$$\\$$ ST is major axis of the ellipse

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