Question

find an equation of the circle that has center (-4, 0) and passes through (5, -3).

Explanation:

Step1: Recall circle equation form

The standard equation of a circle is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius. Here, $h=-4$, $k=0$.

Step2: Calculate radius squared

Use distance formula between center $(-4,0)$ and point $(5,-3)$:
$r^2 = (5 - (-4))^2 + (-3 - 0)^2 = (9)^2 + (-3)^2 = 81 + 9 = 90$.

Step3: Write the circle equation

Substitute $h=-4$, $k=0$, $r^2=90$ into the standard form.

Answer:

$(x + 4)^2 + y^2 = 90$