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An ellipse has its two foci 10 units apart, and the length of its latus rectum is 15. If its axes are taken as the coordinate axes, which equation represents the ellipse?
- 3x² + 4y² = 300
- 2x² + y² = 50
- 10x² + 15y² = 300
- None of these
Correct answer: 3x² + 4y² = 300
Solution
2c=10 -> c=5. Latus rectum 2b^2/a=15 -> b^2=7.5a. With a^2=b^2+25: a^2-7.5a-25=0 -> a=10, b^2=75. Ellipse x^2/100+y^2/75=1 -> 3x^2+4y^2=300.
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