Question

which equation represents a circle with a center at (-5,5) and a radius of 3 units?
a. \\((x + 5)^2 + (y - 5)^2 = 3\\)
b. \\((x - 5)^2 + (y + 5)^2 = 3\\)
c. \\((x + 5)^2 + (y - 5)^2 = 9\\)
d. \\((x - 5)^2 + (y + 5)^2 = 9\\)
e. \\((x + 5)^2 + (y - 5)^2 = 6\\)

Explanation:

Step1: Recall circle standard form

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 $(h,k)=(-5,5)$

Substitute $h=-5$, $k=5$: $(x-(-5))^2+(y-5)^2=r^2$ simplifies to $(x+5)^2+(y-5)^2=r^2$.

Step3: Substitute radius $r=3$

Calculate $r^2=3^2=9$. Substitute to get $(x+5)^2+(y-5)^2=9$.

Answer:

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