Search

Search results:

1.
Circle equation centered at the origin
$x^2+y^2=R^2$
2.
Circle equation centered at (a, b)
$(x-a)^2+(y-b)^2=R^2$
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: $R = \sqrt{\dfrac{D^2+E^2-4AF}{2|A|}}$
8.
Circle perimeter
$P=2r\pi $
9.
Circle area
$A = r^2\pi$
10.
Circle arc - verison 1
$ s = r \cdot x $
11.
Circle arc
$ s = \dfrac{\pi r \alpha}{180\degree} $
12.
Sector area
$ B = \dfrac{r\cdot s}{2} $
13.
Sector area - version 2
$ B = \dfrac {r^2 \cdot x}{2} $
14.
Segment area - verison 1
$ S = \dfrac{1}{2} \left(s r - a(r-h)\right)^2$
15.
Segment area - verison 2
$ S = \dfrac{r^2}{2} \left(\dfrac{\alpha\pi}{180\degree} - \sin\alpha\right)$