Question

Find the equation of the line so that the line segment intercepted between the axes is divided by the point P(-5, 4) in the ratio 1: 2.

Answer 1

Let AB be the given line segment making intercepts a and b on the x-axis and y-axis respectively. Then, the equation of line AB is $\frac{x}{a}+\frac{y}{b}=1$

So, these points are A(a, 0) and B(0, b).

Now, P(-5, 4) divides AB in the ratio 1: 2.

$\therefore \frac{(1\times 0+2\times a)}{(1+2)}$ = - 5 and

$\frac{(1\times b+2\times 0)}{(1+2)}=4\iff a=\frac{-15}{2}andb=12$

So, the required equation of the line is $\frac{x}{\left(\frac{-15}{2}\right)}+\frac{y}{12}=1\iff \frac{-2x}{15}+\frac{y}{12}=1$

$\iff 8x-5y+60=0$