# How do you write the standard from of the equation of the circle given center at (-2,5) and radius of 5?

${x}^{2} + {y}^{2} + 4 x - 10 y + 4 = 0.$
If the centre & radius of circle are (h,k) & r, then, its eqn. is :${\left(x + h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$
Hence, the reqd. eqn. is ${\left(x + 2\right)}^{2} + {\left(y - 5\right)}^{2} = {5}^{2.}$ Simplifying, it becomes,
${x}^{2} + {y}^{2} + 4 x - 10 y + 4 = 0.$