CircleHard

Question

A circle has the same centre as an ellipse & passes through the foci F1 & F2 of the ellipse, such that two curves intersect in 4 points. Let ′P′ be any one of their point of intersection. If the major axis of the ellipse is 17 & the area of the triangle PF1 F2 is 30, then the distance between the foci is -

Options

A.11
B.12
C.13
D.none

Solution

     
Co-ordinate of point P(acosθ, bsinθ).
Also, PF1 + PF2 = 17        ..... (i)
Given PF1. PF2 = 30   ⇒  PF1. PF2 = 60    .... (ii)
From (i) & (ii) PF1 = 5 & PF2 = 12
∴  (F1 F2)2    = (PF1)2 + (PF2)2
            = 52 + 122    ⇒  F1F2 = 13

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