Circle
We found 7 formulas for circle
Variables
R
→
Circle radius
(a,b)
→
Center of a circle
A,B,C...
→
Real Numbers
3.
Three point form
$\begin{vmatrix}
x^2+y^2 & x & y & 1 \\[0.5em]
x_1^2+y_1^2 & x_1 & y_1 & 1 \\[0.5em]
x_2^2+y_2^2 & x_2 & y_2 & 1 \\[0.5em]
x_3^2+y_3^2 & x_3 & y_3 & 1 \\[0.5em]
\end{vmatrix}
$
4.
Parametirc equation of a circle
$\begin{aligned}
x &= a + R\cos t \\
y &= b + R\sin t \\
\end{aligned} ~~~~~~ 0 \le t \le 2\pi $
5.
General circle equation
$Ax^2+Ay^2+DX+Ey+F=0 \text{ where } A \ne 0, D^2+E^2>4AF$
6.
Ceter of a circle
If the circle equation is: $Ax^2+Ay^2+DX+Ey+F=0$ than the cetrer of the circle has coordinates:
$a = -\dfrac{D}{2A}, ~~~ b = -\dfrac{E}{2A} $
7.
Radius of a circle
If the circle equation is: $Ax^2+Ay^2+DX+Ey+F=0$ than the radius is equal:
$R = \sqrt{\dfrac{D^2+E^2-4AF}{2|A|}}$