Question

Write an equation of the circle that has the given center and radius.

$C(-2,5);r=\frac{1}{3}$

Short answer

The equation of the circle is ${\left(x+2\right)}^2+{\left(y-5\right)}^2=\frac{1}{9}$

Step-by-step solution

Step-1 – Given

The given center = C(-2, 5) and radius = r = $\frac{1}{3}.$

Step-2 – To determine

We have to find the equation of the circle.

Step-3 – Calculation 

Given that center =$\left(a,b\right)=\left(-2,5\right)\text{andradiusr}=\frac{1}{3}$ We will plug them in the standard form of a circle formula to get the equation:

${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$

$\begin{array}{l}{\left(x-\left(-2\right)\right)}^2+{\left(y-5\right)}^2={\left(\frac{1}{3}\right)}^2\\ {\left(x+2\right)}^2+{\left(y-5\right)}^2=\frac{1}{9}\end{array}$

So, the equation of the circle is${\left(x+2\right)}^2+{\left(y-5\right)}^2=\frac{1}{9}.$