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Question:

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 is:

2

3

2√2

3√2

Solution:

Equation of circle can be written as (x-1)²+(y-1)²+λ(x-y)=0
If passes through (1,-3)
16+λ(4)=0 ⇒ λ=-4
So (x-1)²+(y-1)²-4(x-y)=0 ⇒ x²+y²-6x+2y+2=0
⇒ r=2√2