Question

write an equation of the circle with center (-2, 4) and diameter 8.

Explanation:

Step1: Recall circle - equation formula

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

Step2: Determine the radius

Given the diameter $d = 8$, the radius $r=\frac{d}{2}=\frac{8}{2}=4$.

Step3: Identify the center - coordinates

The center of the circle is $(h,k)=(-2,4)$.

Step4: Substitute values into the formula

Substitute $h=-2$, $k = 4$, and $r = 4$ into the standard - form equation: $(x-(-2))^2+(y - 4)^2=4^2$.
Simplify to get $(x + 2)^2+(y - 4)^2=16$.

Answer:

$(x + 2)^2+(y - 4)^2=16$