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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