Question

Find equations of altitudes and the co-ordiantes of the othocentre of the triangle whose sides are $3x-2y=6,3x+4y+12=0$ and $3x-8y+12=0$

Answer 1

$3y-4x-16$
$3y-4x+7=0$.............(i)
$3y+2x+8-0$............(ii)
$\left(i\right)+2\left(ii\right)\Rightarrow 9y+23=0$
$\Rightarrow y=\frac{-23}{9}$
$\therefore 3x\frac{-23}{9}-4x+7=0$
$\frac{-23+21}{3}=4x$
$\Rightarrow k=\frac{-2}{12}=\frac{-1}{65}$