Some More Properties of Ellipse
- Circle described on focal length as diameter always touches auxiliary circle.
- Locus of feet of perpendiculars from foci upon any tangent is auxiliary circle.
- Length of tangent between the point of contact and the point where it meets the directrix subtends right angle at the corresponding focus.
- Tangents at the extremities of latus rectum passes through the corresponding foot of directrix on major axis.
- Product of perpendiculars from foci upon any tangent of ellipse = 1 is b2.
- Area of ellipse = 1 is Ïab.
- 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.
- Semi-latus rectum is harmonic mean of segments of focal chord or = (a > b).