Question

what is the equation of a circle with center at (-4,3) and radius 5?
a. (x - 4)^2+(y + 3)^2 = 5
b. (x + 4)^2+(y - 3)^2 = 5
c. (x + 4)^2+(y - 3)^2 = 25
d. (x - 4)^2+(y + 3)^2 = 125

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify the values of $h$, $k$, and $r$

Given that the center is $(-4,3)$ and the radius $r = 5$. So, $h=-4$, $k = 3$, and $r = 5$.

Step3: Substitute the values into the formula

Substitute $h=-4$, $k = 3$, and $r = 5$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-4))^2+(y - 3)^2=5^2$, which simplifies to $(x + 4)^2+(y - 3)^2=25$.

Answer:

C. $(x + 4)^2+(y - 3)^2=25$