Answer:
(x -2)² +(y -5)² = 36
Explanation:
You want the equation of a circle whose diameter has end points (2, 11) and (2, -1).
Center
The circle center will be the midpoint of the diameter segment:
(h, k) = ((2, 11) +(2, -1))/2 = (2+2, 11 -1)/2 = (2, 5)
Radius
The radius is half the length of the diameter. Since the diameter is on the vertical line x=2, the length of it is the difference of the y-coordinates of the end points; 11 -(-1) = 12. Half that is 6, so the radius is 6.
Equation
The standard form equation for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
For (h, k) = (2, 5) and r = 6, the equation is ...
(x -2)² +(y -5)² = 36