# How do you find the standard form of the equation of the circle with center at origin with points (-2,3)?

Dec 8, 2015

${x}^{2} + {y}^{2} = 13$
Any circle centred at $\left(a , b\right)$ and having radius $r$ has equation
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
So in this case the centre is $\left(0 , 0\right)$ and the radius may be found from the given point and Pythagoras as ${r}^{2} = {x}^{2} + {y}^{2} = {2}^{2} + {3}^{2} = 13$.
Hence the equation is ${x}^{2} + {y}^{2} = 13$.