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.
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