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
- A \(2 x^2+2 y^2-2 x-14 y+21=0\)
- B \(x^2+y^2-x-7 y+10=0\)
- C \(2 x^2+2 y^2-x-7 y+21=0\)
- D \(x^2+y^2-2 x-14 y+10=0\)
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…
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