A circle has the same center as an ellipse and passes through the foci F1, and F2 of the ellipse, such that
the two curves intersect at four points. Let P be any one of their points of intersection. If the major axis of the ellipse is
17 and the area of triangle PF1F2 is 30, then the distance between the foci is
13
10
11
None of these
Let the ellipse be x2a2+y2b2=1 . Then the circle is x2+y2=a2e2
Radius of circle =ae
One of the points of intersection of the circle and the ellipse is
ae2e2−1,ae1−e2
Now, area of ΔPF1F2 is
12ae1−e2(2ae)=30 (Given) or a21−e2=30 or a2e2=a2−30=1722−30=1694 or 2ae=13