MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

Answer:D) (x - 3)^2 + (y - 2)^2 = 37Step-by-step explanation:The equation of a circle with center (h, k) and radius r is(x - h)^2 + (y - k)^2 = r^2We 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^2We 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 = 37Answer: D) (x - 3)^2 + (y - 2)^2 = 37