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The equation of the circle passing through the points of intersection of the circles \[ x^2+y^2-2x-4y+1=0, \] \[ x^2+y^2-4x-2y+4=0 \] and having its centre on the line \[ x-2y-3=0 \] is

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If a circle passes through the common points of two circles $S_1=0$ and $S_2=0$, use \[ S_1+\lambda(S_2-S_1)=0. \] Then apply the extra condition (centre, radius, tangent, etc.) to determine $\lambda$.

Updated On: Jul 29, 2026

\[ x^2+y^2-6x+7=0 \]
\[ x^2+y^2+6x+7=0 \]
\[ x^2+y^2+6x-7=0 \]
\[ x^2+y^2-6x-7=0 \]

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The Correct Option is A

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The equation of the circle passing through the points of intersection of the circles \[ x^2+y^2-2x-4y+1=0, \] \[ x^2+y^2-4x-2y+4=0 \] and having its centre on the line \[ x-2y-3=0 \] is

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The Correct Option is A

Solution and Explanation

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