﻿ Find the locus of the point of intersection of the tangents to the ellipse , if the difference of the eccentric angle of their points of contact is 2α. : Kaysons Education

# Find The Locus Of The Point Of Intersection Of The Tangents To The Ellipse , If The Difference Of The Eccentric Angle Of Their Points Of Contact Is 2α.

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## Question

### Solution

Correct option is

Let the point of intersection be (h, k). Let θ1 and θ2 be the eccentric angles such that

θ1 – θ2 = 2α                      … (1)

Points of contacts are  and the equations of tangents at these points are

Since these tangents pass through (h, k)

On solving these equations, we get

.

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