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how to prove that when ellipse and hyperbola intersect orthogonally , they are confocal.

how to prove that when ellipse and hyperbola intersect orthogonally , they are confocal.

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago
First of all, write the equations of hyperbola and ellipse in general form. They intersect at 2 points. Take one point and write the equations of tangent to both ellipse and hyperbola at the point of intersection. As they are orthogonal, hence the slope of both tangents must satisfy :
m1m2 = -1
Hence, from this you will get the result that both are confocal.
Thanks & Regards
Bharat Bajaj
askIITians Faculty

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