Question

writing an equation with a given center and ra
which equation represents a circle with a center at (2, -8) and a radius of 11?
$(x - 8)^2 + (y + 2)^2 = 11$
$(x - 2)^2 + (y + 8)^2 = 121$
$(x + 2)^2 + (y - 8)^2 = 11$
$(x + 8)^2 + (y - 2)^2 = 121$

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 $(2,-8)$

Substitute $h=2$, $k=-8$: $(x-2)^2 + (y-(-8))^2 = r^2$, which simplifies to $(x-2)^2 + (y+8)^2 = r^2$.

Step3: Substitute radius $r=11$

Calculate $r^2 = 11^2 = 121$. Substitute into the equation: $(x-2)^2 + (y+8)^2 = 121$.

Answer:

B. $(x-2)^2 + (y + 8)^2 = 121$