Question

circles
what is the equation of a circle with center (-3,1) and radius 2?
a. ((x - 3)^2 + (y - 1)^2 = 2)
b. ((x - 3)^2 + (y - 1)^2 = 4)
c. ((x + 3)^2 + (y - 1)^2 = 2)
d. ((x + 3)^2 + (y - 1)^2 = 4)

now try one on your own.
the equation of a circle with center ((-5, -4)) and radius 3 is ((x + 5)^2 + (y + 4)^2 = 9).

Explanation:

Step1: Recall circle equation formula

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 center $(-3,1)$

Here $h=-3$, $k=1$, so substitute into the formula: $(x-(-3))^2 + (y-1)^2 = r^2$, which simplifies to $(x+3)^2 + (y-1)^2 = r^2$.

Step3: Substitute radius $r=2$

Calculate $r^2 = 2^2 = 4$, so the equation becomes $(x+3)^2 + (y-1)^2 = 4$.

Answer:

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