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Find the equation of the circle that passes through the points of intersection of the circles x² + y² - 6x + 2y + 4 = 0 and x² + y² + 2x - 4y - 6 = 0 and whose centre lies on the line y = x.

1. 7x² + 7y² - 10x - 10y - 12 = 0
2. x² + y² - 10x - 10y - 12 = 0
3. 7x² + 7y² + 10x + 10y - 12 = 0
4. 7x² + 7y² - 10x - 10y + 12 = 0

Correct answer: 7x² + 7y² - 10x - 10y - 12 = 0

Solution

Forming the family and setting its centre on y = x gives lambda = 4/3, leading to 7x² + 7y² - 10x - 10y - 12 = 0.

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