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TS EAMCET · Maths · Circle

Let the circle \(S=x^2+y^2+2 g x+2 f y+c=0\) touch the positive \(\mathrm{X}\)-axis and the positive Y-axis. Let \((2,4)\) be a point on the circle \(S=0\). If two such circles exist, then the difference of their areas is

  1. A \(104 \pi\)
  2. B \(96 \pi\)
  3. C \(9 \pi\)
  4. D \(41 \pi\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(96 \pi\)

Step-by-step Solution

Detailed explanation

\(x^2+y^2+2 g x+2 f y+c=0\) \(\because\) Circle touch \(X\) and \(Y\) axis, \[ \begin{aligned} & g^2-c=f^2-c=0 \\ & \therefore \quad g=f \\ & x^2+y^2+2 g x+2 g y+g^2=0 \end{aligned} \] \(\because\) Circle pass through \((2,4)\)…