ParabolaHard

Question

Consider ellipse = 1 (a > b) & parabola y2 = 4A(x + 4), A > 0. If vertex of parabola coincideswith one focus of ellipse & latus rectum of parabola coincides with minor axis of ellipse, then-′

Options

A.A = 4
B.ab = 32√5
C.Directrix of parabola is tangent to ellipse
D.a > A > b

Solution

         
- ae = - 4& 2b = 4A
Focus of parabola is (- 4 + A,0)
⇒ A = 4
⇒ b = 2A = 8 & ae = 4
b2 = a2(1 - e2) ⇒ a2 = 80 & e =
Directrix of parabola is x + 4 + A = 0 or x = - 8

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