Question

what is the radius of the circle (x - 17/4)^2 + y^2 = 64? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle - equation formula

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

Step2: Compare with given equation

Given the equation $(x-\frac{17}{4})^2 + y^2=64$, we can rewrite $64$ as $8^2$. So, $r^2 = 64$.

Step3: Solve for the radius

Taking the square - root of both sides of the equation $r^2=64$, we get $r=\sqrt{64}=8$.

Answer:

$8$