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A circle concentric with an ellipse passes through the ellipse's foci F1 and F2 and meets the ellipse in 4 points. Let P be one such intersection point. If the major axis length of the ellipse is 17 and the area of triangle P*F1*F2 is 30, find the distance between the foci.
- 11
- 12
- 13
- none
Correct answer: 13
Solution
Since P sees the diameter F1F2 at a right angle, the right-triangle relations together with the ellipse's focal-sum give 2c = 13.
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