Question

what is the radius of the circle $x^{2}+(y + \frac{20}{3})^{2}=49$? 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: Identify the radius

Given the equation $x^{2}+(y+\frac{20}{3})^{2}=49$, comparing it with the standard - form $(x - 0)^2+(y-(-\frac{20}{3}))^{2}=r^{2}$, we have $r^{2}=49$.

Step3: Solve for the radius

Take the square root of both sides of the equation $r^{2}=49$. Since the radius is non - negative, $r = 7$.

Answer:

$7$