Q1 If the tangentat any point on ellipse x2/a2+y2/b2=1 makes an angleα with the major axis and an angleβ with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosβ/cosα.Q2 A line intersects the ellipse x2/a2+y2/b2=1 at P and Q and the parabola y2=4d(x+a) at R and S. The line segment PQ subtends a right angle at the center of the ellipse.find the locus of the point of intersection of tangents to the parabola at R and S.

Pratham Tamhane , 14 Years ago

Grade 12