Search results:
21.
Point - direction form of a line equation
$\dfrac{x-x_1}{X} = \dfrac{y-y_1}{Y}$
22.
Line in prametric form
$\begin{aligned}
x &= a_1+tb_1 \\[0.3 em]
y &= a_2+tb_2
\end{aligned}$
23.
Line - point distance
The distance from the point $P(x_0,y_0)$ to the line $Ax+By+C=0$ is
$d=\dfrac{|Ax_0 + By_0 + C|}{\sqrt{A^2+B^2}}$
24.
Parallel lines - verison 1
Lines $y=k_1x + b_1$ and $y=k_2x + b_2$ are parralel iff $k_1 = k_2$.
25.
Parallel lines - verison 2
Lines $A_1x+B_1y+C_1=0$ and $A_2x+B_2y+C_2=0$ are parallel iff $\dfrac{A_1}{A_2} = \dfrac{B_1}{B_2}$.
26.
Perpendicular lines - verison 1
Lines $y=k_1x + b_1$ and $y=k_2x+b_2$ are perpendicular iff $k_1\cdot k_2=1$.
27.
Perpendicular lines - verison 2
Lines $A_1x+B_1y+C=0$ and $A_2x+B_2y+C=0$ are perpendicular iff $A_1A_2+B_1B_2=0$.
28.
Angle between two lines - verison 1
$\tan\phi = \dfrac{k_2-k-1}{1+k_1k_2}$
29.
Angle between two lines - version 2
$\cos\phi = \dfrac{A_1A_2+B_1B_2}{\sqrt{A_1^2+B_1^2} \cdot \sqrt{A_2^2+B_2^2}}$
30.
Intersection of two lines
Intersection point of lines $A_1x+B_1y+C_1=0$ and $A_2x+B_2y+C_2=0$ has coordinates
$
x_0 = \dfrac{B_1C_2 - B_2C_1}{A_1B_2-A_2B_1},
y_0 = \dfrac{-A_1C_2 + A_2C_1}{A_1B_2-A_2B_1}
$
33.
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}
$
34.
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 $
35.
General circle equation
$Ax^2+Ay^2+DX+Ey+F=0 \text{ where } A \ne 0, D^2+E^2>4AF$
36.
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} $
37.
Radius of a circle
If the circle equation is: $Ax^2+Ay^2+DX+Ey+F=0$ than the radius is equal:
$R = \sqrt{\dfrac{D^2+E^2-4AF}{2|A|}}$