Question

Write an equation for a circle with center (-5,1) and diameter 8 .

Answer 1

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.