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Find the equation of the circle passing through the points of intersection of x² + y² + 2x + 3y - 7 = 0 and x² + y² + 3x - 2y - 1 = 0, and also through the point (1, 2).

1. x² + y² + 4x - 7y + 5 = 0
2. x² + y² - 4x + 7y - 5 = 0
3. x² + y² + 5x + y - 8 = 0
4. x² + y² + 2x - 5y + 3 = 0

Correct answer: x² + y² + 4x - 7y + 5 = 0

Solution

With S1 + lambda*S2 = 0, putting (1,2) gives 6 + 3*lambda = 0, so lambda = -2; substituting and simplifying yields x² + y² + 4x - 7y + 5 = 0.

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