Question

1. what is the equation of a circle with center (3, 8) and radius 2?

(x - 3)² + (y - 8)² = 2
(x - 3)² + (y - 8)² = 4
(x + 3)² + (y + 8)² = 2
(x + 3)² + (y + 8)² = 4

Explanation:

Step1: Recall circle standard 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.

Step2: Substitute given values

Substitute $h=3$, $k=8$, $r=2$ into the formula:
$(x-3)^2 + (y-8)^2 = 2^2$

Step3: Calculate radius squared

Compute $2^2 = 4$, so the equation becomes:
$(x-3)^2 + (y-8)^2 = 4$

Answer:

C. $(x - 3)^2 + (y - 8)^2 = 4$