The centre of a circle C is at the centre of the ellipse E : a 2 x 2 + b 2 y 2 = 1 , a b . Let C pass through the foci F 1 and F 2 of E such that the circle C and the ellipse E intersect at

Question

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 $F_{2}$ of $E$ 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 $PF_{1} F_{2}$ is 30 and the length of the major axis of E is 17 , then the distance between the foci of E is :

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Answer:

B

Solution:

$\frac{1}{2} PF_{1} \cdot PF_{2} = 30 PF_{1} + PF_{2} = 17 PF_{1} = 12 PF_{2} = 5 F_{1} F_{2} = 13 option (2)$

TestHub · Accepted Answer

​ 2 1 ​ PF 1 ​ ⋅ PF 2 ​ = 30 PF 1 ​ + PF 2 ​ = 17 PF 1 ​ = 12 PF 2 ​ = 5 F 1 ​ F 2 ​ = 13 option ( 2 ) ​

Mathematics - Ellipse Question with Solution | TestHub

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