JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 \(\mathrm{y}\)-axis at the point \(\mathrm{P}\), then the square of the distance of \(\mathrm{P}\) from the centre of \(\mathrm{C}_1\) is :
- A \(2\)
- B \(1\)
- C \(6\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\( S_1: x^2+y^2-2 x-2 y+1=0 \) \( S_2: x^2+y^2+2 x-3=0 \) Common chord \(=S_1-S_2=0 \) \( -4 x-2 y+4=0 \) \( 2 x+y=2 \Rightarrow P(0,2) \) \( d_{(c, p)}^2=(1-0)^2+(2-1)^2=2\)
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