Final answer:
The coordinates of the center of the circle are (-12, -2). The radius of the circle is 10. The equation of the circle in standard form is (x + 12)² + (y + 2)² = 100.
Step-by-step explanation:
To find the coordinates of the center of the circle, we need to find the midpoint of the diameter. The midpoint formula is [(x1 + x2) / 2, (y1 + y2) / 2]. So, plugging in (-4, 4) and (-20, -8), we have [( -4 + -20) / 2, (4 + -8) / 2] = (-12, -2). Therefore, the center of the circle is at (-12, -2).
To calculate the radius of the circle, we need to find the distance between one endpoint of the diameter and the center. The distance formula is √[(x2 - x1)² + (y2 - y1)²]. Plugging in (-4, 4) and (-12, -2), we have √[(-12 - -4)² + (-2 - 4)²] = √[( -8)² + (-6)²] = √[64 + 36] = √100 = 10. Therefore, the radius of the circle is 10.
The equation of a circle in standard form is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. Plugging in (-12, -2) as the center and 10 as the radius, the equation of the circle is (x - (-12))² + (y - (-2))² = 10² simplified to (x + 12)² + (y + 2)² = 100.