The equations of the lines which make intercepts on the axes whose sum is 8 and product is 15 are
The equations of the lines which make intercepts on the axes whose sum is 8 and
product is 15 are
$3 x-5 y+15=0,5 x+3 y+15=0$
$5 x-3 y+15=0,3 x+5 y+15=0$
$3 x+5 y-15=0 \quad, 3 y+5 x-15=0$
$3 x+5 y+15=0,5 x+3 y-15=0$
Solution
Let ' $\mathrm{a}$ ' and ' $\mathrm{b}$ ' be the intercepts made by line.
We have $a+b=8$ and $a b=15$
Solving, we get $(a, b)=(3,5)$ or $(5,3)$
Let equation of line be $\frac{x}{a}+\frac{y}{b}=1$ ...(1)
When $a=3, b=5$ from $(1)$, we get
$\frac{x}{3}+\frac{y}{5}=1 \quad \Rightarrow \quad 5 x+3 y-15=0$ ...(2)
When $a=5, b=3$ from $(1)$, we get
$\frac{x}{5}+\frac{y}{3}=1 \quad \Rightarrow \quad 3 x+5 y-15=0$ ...(3)