Question

a circle has center (8, 0) and passes through (8, 9). which of the following is an equation of the circle?
$x^{2}+(y - 8)^{2}=9$
$x^{2}+(y - 8)^{2}=81$
$(x - 8)^{2}+y^{2}=9$
$(x - 8)^{2}+y^{2}=81$

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle's equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Identify center and calculate radius

Center is $(8,0)$, so $h = 8,k = 0$. Radius $r$ from $(8,0)$ to $(8,9)$ is $r=\sqrt{(8 - 8)^2+(9 - 0)^2}=9$.

Step3: Write the circle's equation

Substitute $h = 8,k = 0,r = 9$ into the formula: $(x - 8)^2+(y - 0)^2=9^2$, which is $(x - 8)^2+y^2=81$.

Answer:

$(x - 8)^2+y^2=81$