Question

what is the equation of a circle with center at (2, -5) and radius 3?
a. (x - 2)^2+(y + 5)^2 = 81
b. (x + 2)^2+(y - 5)^2 = 3
c. (x + 2)^2+(y - 5)^2 = 9
d. (x - 2)^2+(y + 5)^2 = 9

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 values of $h$, $k$, and $r$

Given that the center is $(2,-5)$ and the radius $r = 3$. So, $h = 2$, $k=-5$, and $r = 3$.

Step3: Substitute values into the formula

Substitute $h = 2$, $k=-5$, and $r = 3$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 2)^2+(y-(-5))^2=3^2$, which simplifies to $(x - 2)^2+(y + 5)^2=9$.

Answer:

D. $(x - 2)^2+(y + 5)^2=9$