Question

1. what is the equation of the circle with center at (-1, -3) and radius 4?

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

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 $(-1,-3)$

Here, $h=-1$, $k=-3$. Substitute into the formula:
$(x - (-1))^2 + (y - (-3))^2 = r^2$
Simplify to: $(x+1)^2 + (y+3)^2 = r^2$

Step3: Substitute radius $r=4$

Calculate $r^2 = 4^2 = 16$. The correct equation is $(x+1)^2 + (y+3)^2 = 16$.
Note: All given options have an incorrect right-hand side (2 instead of 16), but Option A has the correct left-hand side matching the center.

Answer:

A. $(x + 1)^2 + (y + 3)^2 = 2$
(Note: The correct right-hand side should be 16, but this is the only option with the correct form for the given center)