Question

The standard equation of a circle with center at $\left(-2,5\right)$and radius $3$is ______ .

Short answer

The standard equation of a circle with center at $\left(-2,5\right)$ and radius$3$is${\left(x+2\right)}^2+{\left(y-5\right)}^2=9.$

Step-by-step solution

Step 1. Given Information 

The given center of a circle is $\left(-2,5\right)$and radius is $3.$

Step 2. Filling the blank 

The standard equation of a circle with center $\left(h,k\right),$and radius $r$is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2.$

So, the standard equation of a circle with center at$\left(-2,5\right)$and radius$3$isrole="math" localid="1646719972363" $$\begin{gathered} {\left(x+2\right)}^2+{\left(y-5\right)}^2=3^2 \\ {\left(x+2\right)}^2+{\left(y-5\right)}^2=9 \end{gathered}$$