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TS EAMCET · Maths · Circle

The equation of the circle whose diameter is the common chord of the circles \(x^2+y^2+2 x+3 y+1=0\) and \(x^2+y^2+4 x+3 y+2=0\) is

  1. A \(2 x^2+2 y^2+2 x+6 y+1=0\)
  2. B \(x^2+y^2-2 x+3 y-1=0\)
  3. C \(x^2+y^2+2 x+3 y-4=0\)
  4. D \(2 x^2+2 y^2-x+2 y+1=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 x^2+2 y^2+2 x+6 y+1=0\)

Step-by-step Solution

Detailed explanation

Common chord of \(S_1\) and \(S_2\) is \(S_1-S_2=0\) \[ \begin{aligned} & \left(x^2+y^2+2 x+3 y+1\right)-\left(x^2+y^2+4 x+3 y+2\right)=0 \\ & \Rightarrow \quad-2 x-1=0 \\ & \therefore \quad x=\frac{-1}{2} \end{aligned} \] Also circle passing through \(S_1\) and \(S_2\)…