Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Condition of Concurrency of three given lines

 L_1: a_1x+b_1y+c_1=0

 L_2: a_2x+b_2y+c_2=0

 L_3: a_3x+b_3y+c_3=0

 L_1,L_2 \text { and } L_3 are concurrent if  a_3(b_1c_2-b_2c_1)+b_3(a_2c_1-a_1c_2)+c_3(a_1b_2-a_2b_1)=0

Distance of a point form a line:

The distance means (perpendicular distance) of a point  P (x_1, y_1) from the line  Ax+By +C=0 is given by

d=\left| \dfrac{Ax_1+By_1+C}{\sqrt{A^2+B^2}} \right|

Distance between two Parallel lines:

The distance between two parallel lines  y=mx+c_1 \text { and } y=mx+c_2 is given by  d=\dfrac{|c_1-c_2|}{\sqrt{1+m^2}}

Note:

 L_1: ax+by+c_1=0

 L_2: ax+by+c_2=0,\quad c_1 \neq c_2

then  d=\dfrac{|c_1-c_2|}{\sqrt{a^2+b^2}}

 

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