How to convert equation of a circle from standard form to general form

Описание: To convert the equation of a circle from standard form to general form, we need to complete the square for both x and y terms.

The standard form of the equation of a circle is:

(x-a)² + (y-b)² = r²

where (a,b) is the center of the circle and r is the radius.

To convert this to general form, we expand the squares and simplify:

(x-a)² + (y-b)² = r²

x² - 2ax + a² + y² - 2by + b² = r²

x² - 2ax + y² - 2by + a² + b² - r² = 0
let a=-f and b=-g
x² +2fx + y² +2gy+ a² + b² - r² = 0

Let c=a²+b²-r²
x² +2fx + y² +2gy+ c = 0

where (-f,-g) is the center of the circle and radius (r) =√(f²+g²-c)