Explanation:
the standard form of a circle equation is
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle, and r is the radius.
so, we have
(x - 1)² + (y - -4)² = r²
(x - 1)² + (y + 4)² = r²
how do we get r or r² ?
by using the coordinates of the point the circle passes through :
(-3 - 1)² + (0 + 4)² = r²
(-4)² + 4² = r²
16 + 16 = r²
32 = r²
so, our equation is
(x - 1)² + (y + 4)² = 32