Final answer:
The equation for a circle with center (-5,1) and diameter 8 is (x + 5)² + (y - 1)² = 16.
Step-by-step explanation:
To write an equation for a circle with center (-5,1) and diameter 8, we can use the standard form equation of a circle, which is:
(x - h)² + (y - k)² = r²
Here, (h, k) represents the coordinates of the center of the circle, and r is the radius of the circle. Given that the diameter is 8, the radius (r) is half of the diameter, hence r = 4. Substituting the given center and radius into the standard form gives us:
(x + 5)² + (y - 1)² = 4²
(x + 5)² + (y - 1)² = 16
This equation represents the circle with the specified center and diameter.