Answer:
(x + 3)^2 + (y + 6)^2 = (√2)^2 = 2
Explanation:
The standard equation for a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2. We need to find h, k and r for this particular circle.
The length of the radius is half the length of the diameter. Find the length of this diameter first, and than halve the result.
diameter^2 = 2^2 + 2^2, or diameter^2 = 8, or diameter = √8 = 2√2.
This is because x changes from -4 to -2 (+2) and y changes from -7 to -5 (+2).
Then the radius is r = 2√2.
The coordinates of the center are found using the midpoint formula:
-4-2
xcenter = -------- = -3
2
-7-5
ycenter = -------- = - 6
2
Inserting -3 for h, -6 for k and √2 for r, we get:
(x + 3)^2 + (y + 6)^2 = (√2)^2 = 2