Question

what is the equation, in standard form, of a circle with center (7, -4) and radius 6? enter your answer by filling in the boxes. (x□)² + (y□)² = □

Explanation:

Step1: Recall circle standard form

Standard form: $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is center, $r$ radius.

Step2: Substitute center values

Center $(7,-4)$: $h=7$, $k=-4$. So $(x-7)^2 + (y+4)^2$.

Step3: Calculate radius squared

Radius $r=6$, $r^2=6^2=36$.

Answer:

$(x-7)^2 + (y+4)^2 = 36$