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Q1 If the tangent at any point on ellipse x 2 /a 2 +y 2 /b 2 =1 makes an angle α with the major axis and an angle β with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosβ/cos α. 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.

Q1 If the tangent at any point on ellipse x2/a2+y2/b2=1 makes an angle α with the major axis and an angle β 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.

Grade:12

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
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