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Consider the two circles C1: x² + y² - 4x + 6y + 11 = 0 and C2: x² + y² - 2x + 8y + 13 = 0. A circle passes through both points of intersection of C1 and C2, and also passes through the origin. Find the x-coordinate of the centre of this circle.

1. (A) -2
2. (B) -1
3. (C) 1/2
4. (D) 2

Correct answer: (C) 1/2

Solution

The family of circles passing through the intersection of C1 and C2 is S = S1 + lambda*(S2 - S1) = 0. Since the required circle also passes through origin, substitute x=0, y=0 to find lambda, then identify the centre.

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