Question

select the correct answer. which equation represents a circle with center z(-3,5) and a radius of 4 units? a. \\((x - 3)^2 + (y + 5)^2 = 4\\) b. \\((x - 3)^2 + (y + 5)^2 = 16\\) c. \\((x + 3)^2 + (y - 5)^2 = 4\\) d. \\((x + 3)^2 + (y - 5)^2 = 16\\)

Explanation:

Step1: Recall circle equation formula

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 $(-3,5)$

Here $h=-3$, $k=5$. Substitute into the formula:
$$(x - (-3))^2 + (y - 5)^2 = r^2$$
Simplify to:
$$(x+3)^2 + (y-5)^2 = r^2$$

Step3: Substitute radius $r=4$

Calculate $r^2$: $4^2=16$. Substitute into the equation:
$$(x+3)^2 + (y-5)^2 = 16$$

Answer:

D. $(x+3)^2 + (y-5)^2 = 16$