Question

Write the equation of the circle with center (3, 2) and with (9, 3) being a point on the circle. A) (x − 3)2 + (y − 2)2 = 13 Eliminate B) (x − 3)2 + (y − 2)2 = 18 C) (x − 3)2 + (y − 2)2 = 25 D) (x − 3)2 + (y − 2)2 = 37

Answer 1

D) (x - 3)^2 + (y - 2)^2 = 37

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