Final answer:
To write the standard form of the equation of a circle with center (2, -3) and radius 8, use the formula (x - h)^2 + (y - k)^2 = r^2 to get (x - 2)^2 + (y + 3)^2 = 64.
Step-by-step explanation:
The student has asked for the standard form of the equation of a circle with a given center and radius. To write the equation of a circle in standard form, you use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Since the center of the circle is at (2, -3) and the radius is 8, we can substitute these values into the formula.
This yields the equation:
(x - 2)^2 + (y + 3)^2 = 8^2
Which simplifies to:
(x - 2)^2 + (y + 3)^2 = 64
This is the standard form equation for the circle described by the student.