(x-1)² + (y +3)² = 16
1) Since the center is at (1,-3) then we can write out:
(x-1)² + (y +3)² = r²
2) Since this circle is tangent to the tangent and vertical line x=-3 Then the radius can be found this way
The distance from the center to this tangent line in absolute value.
r= | x-coordinate - tangent line|
r = | 1 -(-3)|
r =| 1+3|
r = |4|
r = 4
3) Hence, the answer is
(x-1)² + (y +3)² = 4²
(x-1)² + (y +3)² = 16