Final answer:
To find the equation of the circle, we need to find the center and radius of the circle. The midpoint of the diameter is the center of the circle, and the distance from the center to either endpoint is the radius. The equation of the circle is (x-0)²+(y-(-1))²=41.
Step-by-step explanation:
To find the equation of the circle, we need to find the center and radius of the circle. The midpoint of the diameter is the center of the circle, and the distance from the center to either endpoint is the radius.
The midpoint of the diameter is (4+(-4))/2, (-6+4)/2 = 0, -1.
The radius is the distance from the center to either endpoint, which is √((4-0)²+(-6-(-1))²) = √(16+25) = √41.
Therefore, the equation of the circle is (x-0)²+(y-(-1))²=41.