Transform the standard form of a circle equation (x-h)² + (y-k)² = r² into its general form Ax² + By² + Cx + Dy + E = 0 effortlessly. Our online circle equation converter helps students and professionals quickly find the coefficients A, B, C, D, and E from your center (h, k) and radius r values.
Formula:
The Standard Form of a circle's equation is:
(x - h)² + (y - k)² = r²
Where:
h= x-coordinate of the centerk= y-coordinate of the centerr= Radius of the circle
The General Form of a circle's equation is:
Ax² + By² + Cx + Dy + E = 0
To convert, expand the standard form and rearrange terms:
(x - h)²expands tox² - 2hx + h²(y - k)²expands toy² - 2ky + k²- Substitute back:
x² - 2hx + h² + y² - 2ky + k² = r² - Rearrange to match general form:
x² + y² - 2hx - 2ky + (h² + k² - r²) = 0
Comparing this to Ax² + By² + Cx + Dy + E = 0, we get the coefficients:
A = 1B = 1C = -2hD = -2kE = h² + k² - r²