EllipseHard
Question
tangent is drawn from point P(- 4, 0) to the ellipse 
= 1 (a > b) which makes 60o with x-axis. If this tangent intersects its auxiliary circle at points A & B such that AB = 2b, then -
= 1 (a > b) which makes 60o with x-axis. If this tangent intersects its auxiliary circle at points A & B such that AB = 2b, then -Options
A.eccentricity of ellipse is 
B.AB = 2√3
C.distance between foci is (2AB)
D.point P lies on director circle of ellipse
Solution
cos 60o =
1 - e2 =
e =
& b = ∵ y - 0 = tan60o (x + 4) is tangent
∴ c2 = a2m2b2 ⇒ 48 = 3a2 + b2
⇒ a2 = 15 & b2 = 3
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