Tutorial:
Basic + Adv(not very advanced)
Straight line

Question

Tutorial:
Basic + Adv(not very advanced) 
Straight line

rvc · Answer

$\huge\color{red}{\sf Slope\ of\ a\ Line:}$

rvc · Answer

$\large\color{Brown}{1)\ Slope\ of\ the\ line\ passing\ through\ the\ points\ A(x_{1},y_{1})\ and\ B(x_{2},y_{2}):}$
 $\large\color{purple}{m=\frac{ y_{2}-y_{1} }{x_{2}-x_{1}}}$ $\large\color{red}{x_{2}\neq x_{1}}$

rvc · Answer

$\large\color{orange}{If\  \theta  \ is\ the\ inclination\ of\ a\ line\ ,\ its\ slope\ is\ m=\tan \theta    }$

rvc · Answer

$\large\color{gold}{IF\ two\ lines\ having\ slopes\ m_{1}\ and\ m_{2}\ are\ \huge\ perpendicular\ }$ $\large\color{red}{ then\ m_{1}.m_{2}=-1}$

rvc · Answer

$\large\color{gold}{IF\ two\ lines\ having\ slopes\ m_{1}\ and\ m_{2}\ are\ \huge\parallel\ } $
$\large\color{red}{m_{1}= m_{2}}$

rvc · Answer

$\Huge\color{purple}{\sf\ The\ equations\ of\ a\ line:}$

rvc · Answer

$\huge\ Eq^n\ of\ line\ \parallel\ to\ X-axis\ : y=k$

rvc · Answer

$\huge\ Eq^n\ of line\  \parallel\ to\ Y-axis\ :x=k$

$\large\ where\ K\ is\ constant $

rvc · Answer

$\huge\ Eq^n\ of\ line\ with\ slope(m)\ passing $ 

$\huge\ through\ (x_{1},y_{1})\ is\ y-y_{1}=m(x-x_{1}) $

rvc · Answer

$\huge\ Eq^n\ of\ line\ through\ pts\ $

$$\huge\ (x_{1},y_{1})\ and\ (x_{2},y_{2})\ is :$$

$$\huge {\frac{ y-y_{1} }{ x-x_{1} } }={ \frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }}$$ 

$\huge\ Where\ x_{1}\neq\ x_{2}$

rvc · Answer

$\huge\ Eq^n\ of\ line\ having\ slope(m)\ and\ $

$\huge\ y-intercept(c)\ :\ y=mx+c $

rvc · Answer

$\huge\ Eq^n\ of\ line\ making\ non-zero$

$\huge\ intercepts\ a\ and\ b\ on\ X and\ Y axes $

$\huge\ respectively :\  \frac{ x }{ a }+\frac{ y }{ b }=1$

rvc · Answer

$\huge\sf  Eq^n\ of\ line\ such\ that\ perpendicular\ drawn $

$\huge\sf from\ origin\ to\ line\ has\ length(p)\ and\ $

$\huge\sf inclination\ \alpha\ : xcos\alpha+ysin\alpha=p$

rvc · Answer

$\huge\tt General\ eq^n\ of\ line\ is\ of\ the\ form\ $

$\huge\tt ax+by+c=0\ and\ its\ slope\ : \frac{-a}{b}$

$\huge\tt b\neq0$

rvc · Answer

$\Large\tt 1)The\ lines\ ax+by+c=0\ \&\ ax+by+k=0\ are\ always$

$\Large\tt \parallel\ for\ all\ c\ and\ k $

$\Large\tt 2)The\ lines\ ax+by+c=0\ \&\ bx-ay+k=0\ are\ always$

$\Large\tt \perp\ for\ all\ c\ and\ k $

rvc · Answer

$\huge \sf The\ \perp\ distance\ of\ (x_{1},y_{1})\ from\ line$

$\huge\sf ax+by+c=0\ is :\ \left| \frac{ ax_{1}+by_{1}+c }{ \sqrt{a^2+b^2} } \right| $

rvc · Answer

$\huge\tt If\ m_{1}\ \&\ m_{2}\ are\ the\ slopes\ of\ 2\ lines $

$\huge\tt then\ acute\ angle\ \theta\ bet^n\ them\ is\ $

$\huge\tt given\ by\ \tan \theta=\left| \frac{ m_{1}-m_{2} }{ 1+m_{1}m_{2}} \right|\ where $

$\huge\tt m_{1}.m_{2}\neq-1$

rvc · Answer

$\Huge\color{purple}{\frak\ Pair\ Of\ Straight\ Lines}$

rvc · Answer

$\huge\tt The~eq^n~$

$\huge\tt ax^2+2hxy+by^2=0\ represents\ the\ $

$\huge\tt pair~of~straight~lines~passing $

$\huge\tt through~the~origin.$

rvc · Answer

$\huge\tt The\ eq^n\ $

$\huge\tt\ ax^2+2hxy+by^2+2gx+2fy+c=0$

$\huge\tt represents\ the\ general\ eq^n$

$\huge\tt of\  pair\ of\ lines.\ $

rvc · Answer

$\huge\sf The\ straight\ lines\ represented\ by\ the\ eq^n$

$\huge\sf ax^2+2hxy+by^2=0\ are:$

$\huge\ 1)\color{red}{ \parallel}\color{blue}{ if\ h^2-ab=0}$

$\huge\ 2)\color{red}{ \perp}\color{blue}{ if\ a+b=0}$

rvc · Answer

$\huge\sf The\ general\ eq^n\  $

$\huge\sf ax^2+2hxy+by^2+2gx+2fy+c=0$

$\huge\sf represents\ pair\ of\ lines\ if$
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