A circle in the xy-plane has its center at (2, 3). The point (5, 7) is on the circle. What is the area of the circle?

The correct answer is D. The radius of the circle is the distance between its center and any point on the circle. The distance formula is d = √((x2 - x1)² + (y2 - y1)²). The square of the radius, r², can be calculated as r² = (5 - 2)² + (7 - 3)^2. This simplifies to r² = 3² + 4², which is r² = 9 + 16 = 25. The formula for the area of a circle is A = πr^2. Substituting 25 for r² gives A = 25π.

A is incorrect because this is the result of finding the radius, r=5, and then calculating πr instead of πr^2.

B is incorrect because this is the circumference of the circle (C = 2πr = 2π(5) = 10π), not the area.

C is incorrect because this results from incorrectly calculating the square of the radius by adding the coordinate differences before squaring: ((5-2) + (7-3))² = (3+4)² = 49. This value, 49, is then incorrectly used as r² in the area formula.