Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius 2 . If the line of the common chord of $\mathrm{C}_1$ and $\mathrm{C}_2$ intersects the $y$-axis at the point $\mathrm{P}$, then the square of the distance of $\mathrm{P}$ from the centre of…

Question

Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius 2 . If the line of the common chord of $\mathrm{C}_1$ and $\mathrm{C}_2$ intersects the $y$-axis at the point $\mathrm{P}$, then the square of the distance of $\mathrm{P}$ from the centre of $\mathrm{C}_1$ is :

Aicharya · Accepted Answer

$\begin{aligned} & S_1: x^2+y^2-2 x-2 y+1=0 \ & S_2: x^2+y^2+2 x-3=0 \ & 	ext { Common chord }=S_1-S_2=0 \ & -4 x-2 y+4=0 \ & 2 x+y=2 \Rightarrow P(0,2) \ & d_{(c, p)}^2=(1-0)^2+(2-1)^2=2\end{aligned}$

Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius 2 . If…

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