Find an equation for the circle.Endpoints of a diameter (-2, -3), (4, -7)

The equation of a circle is given by (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius.

Step 1: Find the center of the circle The center of the circle is the midpoint of the diameter. The midpoint is given by the average of the x-coordinates and the y-coordinates of the endpoints.

So, h = (-2 + 4)/2 = 1 And, k = (-3 - 7)/2 = -5

So, the center of the circle is (1, -5).

Step 2: Find the radius of the circle The radius of the circle is the distance from the center to either endpoint of the diameter. We can use the distance formula to find this:

r = sqrt[(x2 - x1)² + (y2 - y1)²] = sqrt[(4 - 1)² + (-7 - (-5))²] = sqrt[(3)² + (-2)²] = sqrt[9 + 4] = sqrt[13]

Step 3: Substitute h, k and r into the equation of the circle So, the equation of the circle is (x - 1)² + (y + 5)² = 13.