Question

what is the equation of the circle with a center at (1, - 4) and a diameter of 8 units? enter an answer in each box to complete the equation. be sure to include a plus or minus symbol where needed. (x )^2+(y )^2=

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 the center values

Given the center $(h,k)=(1, - 4)$, so $h = 1$ and $k=-4$. The equation becomes $(x - 1)^2+(y+4)^2=r^2$.

Step3: Calculate the radius

Given the diameter $d = 8$. Since $r=\frac{d}{2}$, then $r = 4$, and $r^2=16$.

Answer:

$(x - 1)^2+(y + 4)^2=16$