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Find the equation of the circle that passes through the foci of the ellipse x²/16 + y²/9 = 1 and has its center at (0, 3).

1. x² + y² - 6y - 7 = 0
2. x² + y² - 6y + 7 = 0
3. x² + y² - 6y - 5 = 0
4. x² + y² - 6y + 5 = 0

Correct answer: x² + y² - 6y - 7 = 0

Solution

Foci are (+/- sqrt 7, 0); radius² = 7 + 9 = 16, giving x² + (y - 3)² = 16, i.e. x² + y² - 6y - 7 = 0.

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