# Eccentricity Of A Ellipse

Geometry Level 4

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

Details:

• $$S$$ is the focus of the ellipse.
• $$PT$$ is the tangent with $$P$$ as the point of contact.
• $$ST$$ is major axis of the ellipse.
×