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A standard ellipse (axes along the coordinate axes) has its minor axis equal to the distance between its foci, and its latus rectum equals 10. Find its equation.
- 2x² + y² = 100
- x² + 2y² = 100
- 2x² + 3y² = 80
- none of these
Correct answer: x² + 2y² = 100
Solution
From b = ae we get b² = a²/2; latus rectum 2b²/a = a = 10, so a² = 100, b² = 50, giving x²/100 + y²/50 = 1, i.e. x² + 2y² = 100.
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