First the equation of the circle should be known :
We want to write the equation of the circle in standard form, which is (x - h)² + (y - k)² = r².
The center of the circle, (h, k), is given as (3, -4). Therefore, h = 3 and k = -4.
The radius of the circle, r, is given as 14.
Substituting h = 3, k = -4, and r = 14 into the equation, we have :
(x - 3)² + (y - (-4))² = 14²
Simplifying the equation gives us the result :
(x - 3)² + (y + 4)² = 196
So, the equation of the circle centered at (3, -4) with radius 14 is (x - 3)² + (y + 4)² = 196.