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

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 coordinates

Given center $(-5,5)$, so $h=-5$, $k=5$. Substitute into the formula:
$(x-(-5))^2+(y-5)^2=r^2$ which simplifies to $(x+5)^2+(y-5)^2=r^2$

Step3: Substitute radius value

Given radius $r=3$, calculate $r^2$:
$r^2=3^2=9$

Step4: Form final equation

Substitute $r^2=9$ into the equation:
$(x+5)^2+(y-5)^2=9$

Answer:

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