Question

1. which of the following equations represents a circle with a center at (-1, 3) and radius 2?

a. $(x - 1)^2 + (y + 3)^2 = 4$
b. $(x + 1)^2 + (y + 3)^2 = 4$
c. $(x + 1)^2 + (y - 3)^2 = 4$
d. $(x - 1)^2 + (y + 3)^2 = 16$

Explanation:

Step1: Recall circle standard form

The standard form 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 center and radius

Given center $(-1,3)$ (so $h=-1$, $k=3$) and radius $2$ (so $r^2=4$). Substitute into the formula: $(x - (-1))^2 + (y - 3)^2 = 2^2$, which simplifies to $(x+1)^2 + (y-3)^2 = 4$.

Answer:

c. $(x + 1)^2 + (y - 3)^2 = 4$