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TS EAMCET · Maths · Circle

The equation of a circle which passes through the points of intersection of the circles \(2 x^2+2 y^2-2 x+6 y-3=0\), \(x^2+y^2+4 x+2 y+1=0\) and whose centre lies on the common chord of these circles is

  1. A \(2 x^2+2 y^2-3 x+4 y-2=0\)
  2. B \(x^2+y^2+2 x+5 y-2=0\)
  3. C \(3 x^2+3 y^2-2 x+4 y-3=0\)
  4. D \(4 x^2+4 y^2+6 x+10 y-1=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 x^2+4 y^2+6 x+10 y-1=0\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & S_1 \equiv 2 x^2+2 y^2-2 x+6 y-3=0 \\ & \Rightarrow x^2+y^2-x+3 y-\frac{3}{2}=0 \\ & S_2 \equiv x^2+y^2+4 x+2 y+1=0\end{aligned}\) Eq of common chord is \(S_1-S_2=0\) i.e. \(-5 x+y-\frac{5}{2}=0\)..(i) Eq. of circle passing through intersections of \(S_1\)…