Question

Find the radius of the circle passing the points $(0,0),(1,0)$ and $(0,1)$

Answer 1

$\begin{array}{c}Standardequationofcircleis\\ \Rightarrow x^2+y^2+2gx+2fy+c=0\\ put\left(0,0\right)\\ c=0\\ put=\left(1,0\right)\\ \Rightarrow 1+0+2g+c=0\\ \Rightarrow 2g+1=0\\ \Rightarrow g=\frac{-1}{2}\\ put\left(0,1\right)\\ \Rightarrow 0+1+0+2f+c=0\\ 2f+1=0\\ f=\frac{-1}{2}\\ Radius=\sqrt{f^2+g^2-c}=\sqrt{{\left(-\frac{1}{2}\right)}^2+{\left(-\frac{1}{2}\right)}^2-0}=\sqrt{\frac{1}{4}+\frac{1}{4}}=\frac{1}{\sqrt{2}}\end{array}$