Question

Find the equation of line which passes through the point (- 3 , 8) and cuts off +ive intercepts on the axes whose sum is 7.

Answer 1

Here $a+b=7and-3/a+8/b=1asx/a+y/b=1$ passes through $(-3,8).$
$\therefore$ $-3b+8a=ab$ but $b=7-a$
$\therefore$ $-(7-a)+8a=a(7-a)$
or $a^2+4a-21=0$
$\therefore$ $(a+7)(a-3)=0$ ; $\therefore$ $a=3,-7$
Since the intercepts are + ve ;
$\therefore$ $a=3$ , hence $b=7-a=4$
hence the equation is
$\frac{x}{3}+\frac{y}{4}$ = 1 or $4x+3y=12$