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
Step-by-step explanation:
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
[tex]k=\dfrac{5+7}{2}=\dfrac{12}{2}=6\\\\\\r=|Center-endpoint|\\.\ =|6-5|\\.\ =1[/tex]
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
[tex]h=\dfrac{2+10}{2}=\dfrac{12}{2}=6\\\\\\r=|Center-endpoint|\\.\ =|6-2|\\.\ =4[/tex]
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
[tex]k=\dfrac{14+(-8)}{2}=\dfrac{6}{2}=3\\\\\\r=|Center-endpoint|\\.\ =|3-(-8)|\\.\ =11[/tex]
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
