The locus of the centres of circles passing through the two intersection points of $x^2 +y^2 = 1$ and $x^2 + y^2 - 2x + y = 0$ is:
Step-by-Step Solution
Key Concept: Use the family $S_1 + \lambda(S_2 - S_1) = 0$. Write the general member, extract the centre $(-g, -f)$ in terms of $\lambda$, and eliminate $\lambda$. You get $h + 2k = 0$, i.e., $x + 2y = 0$.
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Correct Answer: (3)