#### Angle Bisector

Angle bisector is locus of point $P(h,k)$ which move such that perpendicular distance of point from lines $L_1=0$ and $L_2=0$ are equal. If the lines $L_1\,:\,a_1x+b_1y+c_1=0$ and $L_2\,:\,a_2x+b_2y+c_2=0$ intersect at point $Q$ i.e $\vert \cfrac{a_1h+b_1k+c_1}{\sqrt{a_1^2+b_1^2}} \vert = \vert \cfrac{a_2h+b_2k+c_2}{\sqrt{a_2^2+b_2^2}} \vert$ Now Replace $(h,k)\rightarrow (x,y)$ we get bisectors $B_1=0\;,\;B_2=0$. $$\Rightarrow \Bigl( \cfrac{a_1x+b_1y+c_1}{\sqrt{a_1^2+b_1^2}}\Bigr)=\pm \Bigl( \cfrac{a_2x+b_2y+c_2}{\sqrt{a_2^2+b_2^2}}\Bigr)$$ Let […]

#### Distance of a point from line.

Shortest distance of a point with respect to line is along the perpendicular to line

#### Principle of Inclusion and Exclusion .

Inclusion and Exclusion principle The principle of inclusion and exclusion  is a counting technique in which the elements satisfy at least one of the different properties while counting elements satisfying more than one property are counted exactly once. For example if we want to count number of numbers in first $100$ natural numbers which are either […]

#### Concept of rotation

Concept of Rotation – As multiplying a complex number by $e^{i\alpha}$ Let $Z = r.e^{i\theta}$ is a non zero complex number where $r=\vert Z \vert$ and $\theta = arg(Z)$. $\therefore$ when we multiply $e^{i\alpha}$ to Z we get a complex number Say $W=Ze^{i\alpha}=r.e^{i(\alpha + \theta)}$ $\therefore$ Geometrically $Z.e^{i\alpha} = W$ can be obtained by […]

#### Distribution of distinct Objects.

Permutation and combination :: Distribution of distinct objects into group having variable group size and fixed group size.

What is a parabola Parabola is a conic section defined as, Locus of a point which moves such that its distance from a fixed point is always in a constant ratio to its perpendicular distance from a fixed line, is called a conic section. $$\frac{PS}{PM}=e\,\,\,\,\,(Constant)$$ where ‘e’ is called as eccentricity of conic section , […]