Question

the graph of the equation below is a circle. what is the length of the radius of the circle? (x - 4)^2+(y + 12)^2=17^2 a. 289 b. 8.5 c. 17 d. 34

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle 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 - squared value

Given the equation $(x - 4)^2+(y + 12)^2=17^2$, comparing it with the standard form $(x - a)^2+(y - b)^2=r^2$, we can see that $r^2 = 17^2$.

Step3: Calculate the radius

Taking the square - root of both sides of the equation $r^2=17^2$, we get $r = 17$ (we consider the positive value since the radius is a non - negative quantity).

Answer:

C. 17