Answer:
The standard form: x² + (y + 1)² = 25
The general form: x² + y² + 2y - 24 = 0
Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (0, -1) and the radius r = 5 (look at the picture).
Substitute:
[tex](x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25[/tex]
use (a + b)² = a² + 2ab + b²
[tex]x^2+y^2+2y+1=25[/tex] subtract 25 from both sides
[tex]x^2+y^2+2y-24=0[/tex]
