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TS EAMCET · Maths · Circle

The equation of the circle inscribed in a square formed by the lines \(x+y-2=0, x+y-6=0, x-y+1=0\) and \(x-y+5=0\) is

  1. A \(2 x^2+2 y^2-2 x-14 y+21=0\)
  2. B \(x^2+y^2-x-7 y+10=0\)
  3. C \(2 x^2+2 y^2-x-7 y+21=0\)
  4. D \(x^2+y^2-2 x-14 y+10=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 x^2+2 y^2-2 x-14 y+21=0\)

Step-by-step Solution

Detailed explanation

Distance between lines \(x+y-2=0\) and \(x+y-6=0\) \[ d=\frac{|-2+6|}{\sqrt{1+1}}=\frac{4}{\sqrt{2}}=2 \sqrt{2} \] \(\therefore \quad\) Radius of circle \(=\frac{d}{2}=\sqrt{2}\) Solving \(x+y-2=0\) and \(x-y+1=0\) \[ \Rightarrow A\left(\frac{1}{2}, \frac{3}{2}\right) \] Solving…