Question

Find what straight lines are represented by the following equation and determine the angles between them.
$x^2-7xy+12y^2=0$

Answer 1

$x^2-7xy+12y^2=0$

Factorising the equation

$x^2-4xy-3xy+12y^2=0x(x-4y)-3y(x-4y)=0(x-4y)(x-3y)=0x=4y,x=3yy=\frac{x}{4},y=\frac{x}{3}$

Slope of first line $m_1=\frac{1}{4}$

Slope of second line $m_2=\frac{1}{3}$

Angle between two straight lines is given by

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=\left|\frac{\frac{1}{4}-\frac{1}{3}}{1+\frac{1}{4}.\frac{1}{3}}\right|$

$\tan \theta =\frac{\frac{1}{12}}{\frac{13}{12}}=\frac{1}{13}\therefore \theta ={\tan }^{-1}\left(\frac{1}{13}\right)$