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An ellipse has eccentricity e = 1/2, the y-axis as a directrix, and the corresponding focus at (3, 0). Find the equation of its auxiliary circle.
- x² + y² - 8x + 12 = 0
- x² + y² - 8x - 12 = 0
- x² + y² - 8x + 9 = 0
- x² + y² = 4
Correct answer: x² + y² - 8x + 12 = 0
Solution
The center is at (4, 0) with a = 2, so the auxiliary circle is (x - 4)² + y² = 4, i.e. x² + y² - 8x + 12 = 0.
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