Final answer:
The question requires identifying which option represents the standard form of a circle's equation. Option A, x^2 + y^2 = 1041, is closest to the standard form resembling a circle centered at the origin with radius √1041. The other options are not valid equations for a circle in standard form.
Step-by-step explanation:
The question asks to write the equation of a circle in standard form. The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. None of the provided options A, B, C, or D represent the standard form of a circle as they either lack the center coordinate terms or have incorrect signs and expressions.
Option A, x^2 + y^2 = 1041, is the closest to the standard form and would represent a circle with a center at (0,0) and a radius of √1041, because when the center is at the origin, the equation simplifies to x^2 + y^2 = r^2. Options B, C, and D are either incomplete, include an extra term, or the radius squared is negative, which is not possible for a real circle.