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Question
Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.
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Solution
It passes through (1, 1) and (2, 2).
∴ \[2g + 2f + c = - 2\]...(1)
And,
\[ \Rightarrow g^2 + f^2 = 1 + c = 5\]
\[ \Rightarrow \left( g + f \right)^2 - 2gf = 5\]
\[ \Rightarrow gf = 2\]
Hence, there are two such circles.
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