Convert form standard to general form for circle.
Circle with center (a,b) and radius c.
standard form - (x-a)^2+(y-b)^2=c^2
can someone simplify this instead then?
x^2-2ax+a^2+y^2-2by+b^2-c^2=0? to make it general form
they are exactly the same equation.
To convert the standard form equation of a circle into the general form, follow the steps below:
Standard form equation: (x - a)^2 + (y - b)^2 = c^2
1. Expand the equation:
(x - a)(x - a) + (y - b)(y - b) = c^2
(x^2 - 2ax + a^2) + (y^2 - 2by + b^2) = c^2
2. Rearrange the terms:
x^2 - 2ax + y^2 - 2by + (a^2+b^2-c^2) = 0
3. Combine the constant terms:
General form equation: x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - c^2) = 0
Therefore, the general form equation of a circle with center (a, b) and radius c is x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - c^2) = 0.