Question

Find what straight lines are represented by the following equation and determine the angles between them.
$4x^2-24xy+11y^2=0$

Answer 1

${4x}^2-24xy+11y^2=0$

Factorising the equation

${4x}^2-2xy-22xy+11y^2=02x(2x-y)-11y(2x-y)=0(2x-y)(2x-11y)=02x=y,2x=11y\Rightarrow y=2x,y=\frac{2}{11}x$

Slope of first line $m_1=2$

Slope of second line $m_2=\frac{2}{11}$

Angle between two straight line

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=\left|\frac{2-\frac{2}{11}}{1+2.\frac{2}{11}}\right|$

$\tan \theta =\frac{\frac{20}{11}}{\frac{15}{11}}=\frac{20}{15}=\frac{4}{3}\theta ={\tan }^{-1}\left(\frac{4}{3}\right)$