Find the equation of the circle with
Centre (1,1) and radius $\sqrt{2}$

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Solution

Here $h = 1, k = 1 a n d r = \sqrt{2}$
the equation of circle is
$(x - h)^{2} + (y - k)^{2} = r^{2} ∴ (x - 1)^{2} + (y - 1)^{2} = (\sqrt{2})^{2} \Rightarrow x^{2} + 1 - 2 x + y^{2} + 1 - 2 y = 2 \Rightarrow x^{2} + y^{2} - 2 x - 2 y = 0$
Which is required equation of circle.

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