Mathematics

Problem

The centre of a circle

C

is at the centre of the ellipse

E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

a > b

. Let

C

pass through the foci

F_1

and

F_2

E

such that the circle

C

and the ellipse

E

intersect at four points. Let

P

be one of these four points. If the area of the triangle

PF_1F_2

is 30 and the length of the major axis of

E

is 17, then the distance between the foci of

E

is: