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Some More Properties of Ellipse

  1. Circle described on focal length as diameter always touches auxiliary circle.
  2. Locus of feet of perpendiculars from foci upon any tangent is auxiliary circle.
  3. Length of tangent between the point of contact and the point where it meets the directrix subtends right angle at the corresponding focus.
  4. Tangents at the extremities of latus rectum passes through the corresponding foot of directrix on major axis.
  5. Product of perpendiculars from foci upon any tangent of ellipse 73266.png = 1 is b2.
  6. Area of ellipse 73260.png = 1 is πab.
  7. Ratio of area of any triangle PQR inscribed in ellipse and that of triangle formed by corresponding points on the auxiliary circle is b/a.
  8. Semi-latus rectum is harmonic mean of segments of focal chord or 73254.png = 73248.png (a > b).

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