[ y² + 16y + 64 ] + [x² - 4x + 4 ] = - 43 + 68

[ y + 8 ]² + [ x - 2 ]² = 25

C (- 8 , 2) and r = 5

y² + x² - 4x + 16y + 43 = 0

regroup terms

(x²-4x) + (y²+16y) = -43

complete the squares

(x²-4x+2²) + (y²+16y+8²) = -43 + 2² + 8²

(x-2)² + (y-8)² = 25

(x-2)² + (y-8)² = 5²

center (2,8)

radius = 5

... except it's (y + 8)² not (y - 8)² so the center is (2, -8)