Question

The perpendicular from the origin to a line meets it at the point $(-2,9)$, find the equation of the line.

Answer 1

Slope of the perpendicular from the point$\left(-2,9\right)$ on the line is,

$m=\frac{-9}{2}$

Let the slope of the required line be $m_1$, then,

$m{m}_1=-1$

$m_1=\frac{2}{9}$

Then the equation of line passing through the point $\left(-2,9\right)$and having slope$\frac{2}{9}$ is given by,

$y-9=\frac{2}{9}\left(x+2\right)$

$9y-81=2x+4$

$2x-9y+85=0$