A circle is tangent to the x-axis and to the y-axis. The coordinates (September 2023 - G01)

Correct answer: G. (0,8).

Since the circle is tangent to both the x and y-axis, and the center coordinates are positive, we can determine the following:
Radius: The radius of the circle is equal to the distance between the center and either the x-axis (tangency point) or the y-axis (tangency point).

Area Formula: We are given that the area of the circle is 64π. The area of a circle is calculated using the formula: Area = π * radius^2.

Solve for Radius: Substitute the given area (64π) into the formula and solve for the radius (r):
64π = π * r^2

Divide both sides by π to isolate r^2:
r^2 = 64

Take the square root of both sides to find the radius (be aware that squaring a negative number also results in a positive answer, so consider both positive and negative square roots):
r = ±√64

Since the radius cannot be negative, we discard the negative solution.
r = √64 = 8

Tangency Point on y-axis: Since the radius represents the distance between the center (which is on a positive y-coordinate) and the tangency point on the y-axis, the y-coordinate of the tangency point is simply the radius itself.