Question

If the intercept of a line between the coordinate axes is divided by the point $(-5,4)$ in the ration $1:2$, then find the equation of the line.

Answer 1

Using division ratio we have

$-5=\frac{2a+0}{3}$

$a=-\frac{15}{2}$ ………….$\left(1\right)$ and $4=\frac{b}{3}$

$b=12$ ………….$\left(2\right)$

now equation of line AB passing through $B(0,12)$ and $P(-5,4)$ is

$y-12=\frac{-8}{-5}x$

$5y-60=8x$

$8x-5y+60=0$ …………$\left(3\right)$

Hence equation of line is $8x-5y+60=0$.