Question

Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on x and y-axes such that a - b = 2

Answer 1

$\text{The equation of line is}$

$\frac{x}{a}+\frac{y}{b}=1$

$\text{Here,}$

$a-b=2$

$ora=2+b$

$\therefore \frac{x}{b+2}+\frac{y}{b}=1...\left(i\right)$

$\text{It passes through (3, 2)}$

$\therefore \frac{3}{b+2}+\frac{2}{b}=1$

$3b+2b+4=b^2+2b$

$\Rightarrow b^2-3b-4=0$

$\Rightarrow b=4or-1$

$\text{Now for}b=4,a=4+2=6$

$forb=-1,a=-1+2=1$

$\therefore a=6or1$

$\therefore \text{Equations of lines are}$

$\frac{x}{6}+\frac{y}{4}=1$

$\Rightarrow 2x+3y=12$

$\frac{x}{1}-\frac{y}{1}=1$

$\therefore x-y=1$