Answer:
D) (x - 3)^2 + (y - 2)^2 = 37
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2
We are given the center (3, 2), so we have h = 3, and k = 2.
The equation is now:
(x - 3)^2 + (y - 2)^2 = r^2
We need to find the radius.
The radius of a circle is the distance from the center of the circle to any point on the circle. We know the center, (3, 2), and we know a point on the circle, (9, 3). We can use the distance formula to find the distance between the center and that point which is the radius of the circle.
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
d = sqrt[(9 - 3)^2 + (3 - 2)^1]
d = sqrt(6^2 + 1^2)
d = sqrt(37)
Now that we have the radius, we apply it to the equation of the circle.
(x - 3)^2 + (y - 2)^2 = (sqrt(37))^2
(x - 3)^2 + (y - 2)^2 = 37
Answer: D) (x - 3)^2 + (y - 2)^2 = 37
