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AP EAMCET · Maths · Circle

Find the equation of a circle which passes through the point \((1,2)\) and the points of intersection of the circles \(x^2+y^2-8 x-6 y+21=0\) and \(x^2+y^2-2 x-15=0\)

  1. A \(x^2+y^2-6 x-4 y+9=0\)
  2. B \(x^2+y^2-18 x-12 y+27=0\)
  3. C \(2\left(x^2+y^2\right)-18 x+12 y+27=0\)
  4. D \(4\left(x^2+y^2\right)-3 x+12 y+16=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^2+y^2-6 x-4 y+9=0\)

Step-by-step Solution

Detailed explanation

\[ \begin{gathered} C_1: x^2+y^2-8 x-6 y+21=0 \\ C_2: x^2+y^2-2 x-15=0 \end{gathered} \] Equation of circle passing through the point of intersection. \[ \begin{gathered} S_1+\lambda S_2=0 \\ \left(x^2+y^2-8 x-6 y+21\right)+s\left(x^2+y^2-2 x-15\right)=0 \end{gathered} \] Now,…