Conic Sections - Ellipse

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Published on February 27, 2014

Author: ednexa



Conic Sections - Ellipse by

Ellipse 1. Equation of the tangent to the ellipse i. at P (x1, y1) is ii. at P (θ) is x 2 y2  1 a 2 b2 xx1 yy1  2 1 a2 b x y cos   sin   1 a b iii. in terms of slope m is y = mx  point of contact is P   a m , b  .   2  c c  at P (θ) is x 2 y2  1 a 2 b2 at P (x1,y1) is ii. and 2 2. Equation of the normal to the ellipse i. a 2m2  b2 a 2 x b2 y   a 2  b2 x1 y1 ax by   a 2  b2 . cos  sin  3. Equation of the director circle of the ellipse is x2 + y2 = a2 + b2. 4. If the tangent at P on the ellipse meets the directrix in F, then PF subtends a right angle at the corresponding focus.

5. The tangent and normal at any point of the ellipse bisect the external and internal angles between the focal radii to that point. 6. The product of the lengths of perpendicular segments from the foci an any tangent to the ellipse x  y  1 is b2. 2 2 a2 b2 Keep on visiting for more study materials. -Team Ednexa

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