Final answer:
To write the equation of a circle with a given center and radius in a specific form, we can use the given information about A, and substitute the values of the center into the equation to find the values of D and F. In this case, D = -1 and F = 5.
Step-by-step explanation:
To write the equation of a circle with center (1, -3) and radius 6 in the form Ax² + Bxy + Cy² + Dx + Ey + F = 0, we need to determine the values of D and F. Since A = 1, we can substitute the values of the center into the equation to find the values of D and F. The equation would be (x - 1)² + (y + 3)² = 36. Expanding this equation and rearranging terms, we get x² + y² - 2x + 6y - 2Dx - 2Ey + 10 = 0. Comparing this equation with the given form, we can conclude that D = -1 and F = 5.