Question

question 10 of 10
which equation describes the circle having center point (3,7) and radius r = 4 in standard form?
a. (x + 3)^2+(y + 7)^2 = 16
b. (x + 3)^2+(y + 7)^2 = 4
c. (x - 3)^2+(y - 7)^2 = 4
d. (x - 3)^2+(y - 7)^2 = 16

Explanation:

Step1: Recall the standard - form of a circle equation

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 values of $a$, $b$, and $r$

Given that the center of the circle is $(3,7)$ and the radius $r = 4$. So, $a = 3$, $b = 7$, and $r^2=4^2 = 16$.

Step3: Substitute the values into the standard - form

Substituting $a = 3$, $b = 7$, and $r^2 = 16$ into $(x - a)^2+(y - b)^2=r^2$, we get $(x - 3)^2+(y - 7)^2=16$.

Answer:

D. $(x - 3)^2+(y - 7)^2=16$