The line x=y touches a circle at the point (1,1). If the circle also passes through the point (1,−3), then its radius(in units) is
A
2
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B
3
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C
2√2
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D
3√2
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Solution
The correct option is C2√2 We know that, the equation of family of circles touching a line L at (x1,y1) is : (x−x1)2+(y−y1)2+λL=0 ⇒(x−1)2+(y−1)2+λ(x−y)=0
The circle also passes through (1,−3) ∴0+16+4λ=0⇒λ=−4
Therefore, the equation of the circle is x2+y2−6x+2y+2=0⇒r=√(−3)2+12−2=2√2