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Find the equation of the circle that passes through the points of intersection of the circles x² + y² - 2x - 4y - 4 = 0 and x² + y² - 10x - 12y + 40 = 0, and whose radius is 4.

1. x² + y² - 2y - 15 = 0
2. x² + y² - 2x - 4y - 4 = 0
3. x² + y² - 4x - 6y + 4 = 0
4. x² + y² - 8x - 10y + 40 = 0

Correct answer: x² + y² - 2y - 15 = 0

Solution

Using the family of circles through the intersection points and imposing r = 4 gives k = 1/4, yielding x² + y² - 2y - 15 = 0 (centre (0, 1), radius 4).

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