Coordinate Geometry

Gradient
m=\dfrac{y_1-y_2}{x_1-x_2}
Equation
y-y_1=m(x-x_1)
y=mx+c
Midpoint
\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)
Parallel Lines
m_1=m_2
Perpendicular Lines
m_1=-\dfrac{1}{m_2}
m_1\times m_2=-1
Area Of Quadrilateral
A=\frac{1}{2}\left| \begin{array}{ccccc} x_1 & x_2 & x_3 & x_4 & x_1\\ y_1& y_2 & y_3 & y_4 & y_1\end{array} \right|
=\frac{1}{2}|(x_1y_2+x_2y_3+x_3y_4+x_4y_1)
-(x_2y_1+x_3y_2+x_4y_3+x_1y_4)|
Note: coordinates should be in anti-clockwise direction
Circle
(x-a)^2+(y-b)^2=r^2
(a,b): centre of circle
r: radius
Circle (Second Formula)
x^2+y^2+2gx+2fy+c=0
(-g,-f): centre of circle
\sqrt{f^2+g^2-c}: radius
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