A chord of ellipse 
whose eccentric angles of extremities are α α and β β , intersects its director circle at point A and B. Tangents at A and B intersect at point P. Find the equation of circumcircle of triangle ABP.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Equation of line AB is 
.
Family of circle passing through point A and B is
= 0 ……(1)
∠ ∠ OAP = ∠ ∠ OBP = 
.
Therefore AOBP is a cyclic quadrilateral i.e. circumcircle of Δ Δ APB will also pass through origin. Satisfying equation (1) by origin, we get
λ λ = 
.
Since the equation of circumcircle of Δ Δ ABP is
= 0.
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