In the coordinate plane, a circle has center (2, -3)…
The area of a circle is A = πr^2. If we can find the radius, then we can find the area of the circle. Recall that the radius is the distance between the center of the circle and any point of the circle on the circumference. Since the center of the circle is (2, -3) and the point (5, 0) is on the circumference, the distance between these two points is the radius of the circle.
Recall that the distance formula is d = [(x_2 – x_1)^2 + (y_2 – y_1)^2]. We can use this formula to determine the radius.
r = [(5 – 2)^2 + (0 – (-3))^2]
r = (3^2 + 3^2)
r = (9 + 9)
r = (18)
Thus, the area of the circle is:
A = π[(18)]^2
A = π(18)
A = 18π