Answer:
(x -6)² +(y +2)² = 128
Explanation:
You want the equation of the circle centered at (6, -2) through point (14, 6).
Circle equation
The equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
For center (h, k) = (6, -2), we can find the value of r² knowing that it will be the value that lets the point (14, 6) satisfy the equation.
(14 -6)² +(6 -(-2))² = r² = 8² +8² = 128
The circle equation is ...
(x -6)² +(y +2)² = 128