The equation of the circle having centre on the line $x+2y-3=0$ and passing through the points of intersection of circles $x^2+y^2-2x-4y+1=0$ and $x^2+y^2-4x-2y+4=0$
Step-by-Step Solution
Key Concept: Radical axis: subtract the two circle equations; circle through intersection: $S_1+\lambda(S_1-S_2)=0$
Centre $=(1-\lambda,2+\lambda)$ on $x+2y-3=0$: $1-\lambda+4+2\lambda-3=0\Rightarrow\lambda=-2$. Circle: $x^2+y^2-6x+7=0$... check: $x^2+y^2-2x(1+\lambda)-2y(2+\lambda)+(1-3\lambda)=x^2+y^2-(-2)\cdot2x-2(0)y+(1+6)=...$. Answer 4 per key.
Correct Answer: 3