Question

Find the equation of a line, given that the foot of the perpendicular from origin to the line is $N(3,-4)$.

Answer 1

Slope $AB=\frac{-4-0}{3-0}=\frac{-4}{3}$

$\therefore$ slope of line $=\frac{3}{4}$

$\therefore y=\frac{3}{4}x+C$ (3, -4) lies on this line

$-4=\frac{9}{4}+C$

$-16=9+4C$

$C=\frac{-25}{4}$

$\therefore$ live is $y=\frac{3x-25}{4}$

$\Rightarrow 3x-4y-25=0$