Question

Find the equations of the straight line which passes through the point $(-3,8)$ and cut positive intercepts on the coordinates axes whose sum is $7$.

Answer 1

Equation of line is intercept from is $\frac{x}{a}+\frac{y}{b}=1$

It passes through $(-3,8)$

$\frac{-3}{a}+\frac{8}{b}=1a+b=7b=7-a\frac{-3}{a}+\frac{8}{7-a}=1a^2+7a-21=0(a-3)(a+7)=0a=-3,7$

For positive intercept $=a=3$

$\Rightarrow b=4$

So the equation of line is

$\frac{x}{3}+\frac{y}{4}=14x+3y-12=0$