Answer: 1. (x + 5)² + (y - 6)² = 1
2. (x - 6)² + (y + 9)² = 16
3. (x + 9)² + (y - 3)² = 121
<u>Step-by-step explanation:</u>
The standard equation of a circle is (x - h)² + (y - k)² = r²
- (h, k) is the Center
- The center is the midpoint of the endpoints
- r is the radius
- radius is the distance from the center to the endpoint
1) endpoints: (-5, 5) and (-5, 7) → h = -5
![k=\dfrac{5+7}{2}=\dfrac{12}{2}=6\\\\\\r=|Center-endpoint|\\.\ =|6-5|\\.\ =1](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B5%2B7%7D%7B2%7D%3D%5Cdfrac%7B12%7D%7B2%7D%3D6%5C%5C%5C%5C%5C%5Cr%3D%7CCenter-endpoint%7C%5C%5C.%5C%20%3D%7C6-5%7C%5C%5C.%5C%20%3D1)
Now input (h, k) = (-5, 6) and r = 1 into the standard equation
(x + 5)² + (y - 6)² = 1² → (x + 5)² + (y - 6)² = 1
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2) endpoints: (2, -9) and (10, -9) → k = -9
![h=\dfrac{2+10}{2}=\dfrac{12}{2}=6\\\\\\r=|Center-endpoint|\\.\ =|6-2|\\.\ =4](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B2%2B10%7D%7B2%7D%3D%5Cdfrac%7B12%7D%7B2%7D%3D6%5C%5C%5C%5C%5C%5Cr%3D%7CCenter-endpoint%7C%5C%5C.%5C%20%3D%7C6-2%7C%5C%5C.%5C%20%3D4)
Now input (h, k) = (6, -9) and r = 4 into the standard equation
(x - 6)² + (y + 9)² = 4² → (x - 6)² + (y + 9)² = 16
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3) endpoints: (-9, 14) and (-9, -8) → h = -9
![k=\dfrac{14+(-8)}{2}=\dfrac{6}{2}=3\\\\\\r=|Center-endpoint|\\.\ =|3-(-8)|\\.\ =11](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B14%2B%28-8%29%7D%7B2%7D%3D%5Cdfrac%7B6%7D%7B2%7D%3D3%5C%5C%5C%5C%5C%5Cr%3D%7CCenter-endpoint%7C%5C%5C.%5C%20%3D%7C3-%28-8%29%7C%5C%5C.%5C%20%3D11)
Now input (h, k) = (-9, 3) and r = 11 into the standard equation
(x + 9)² + (y - 3)² = 11² → (x + 9)² + (y - 3)² = 121