Question

use the center and radius provided to write the equation of a circle.
center: $(-2, 5)$
radius: 5

Explanation:

Step1: Recall circle equation form

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

Step2: Substitute center values

Here, $h=-2$, $k=5$, so substitute into the formula:
$(x-(-2))^2 + (y-5)^2 = r^2$
Simplify to: $(x+2)^2 + (y-5)^2 = r^2$

Step3: Substitute radius value

Given $r=5$, calculate $r^2$:
$r^2 = 5^2 = 25$
Substitute into the equation: $(x+2)^2 + (y-5)^2 = 25$

Answer:

$(x+2)^2 + (y-5)^2 = 25$