CircleMedium
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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