**Question:**

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.

**Solution:**

Let the intercepts cut by the given lines on the axes be *a *and *b*.

It is given that

*a* + *b* = 1 … (1)

*ab* = –6 … (2)

On solving equations (1) and (2), we obtain

*a* = 3 and *b* = –2 or *a *= –2 and *b* = 3

It is known that the equation of the line whose intercepts on the axes are *a* and *b* is

$\frac{x}{a}+\frac{y}{b}=1$ or $b x+a y-a b=0$

Case I: *a* = 3 and *b* = –2

In this case, the equation of the line is –2*x* + 3*y* + 6 = 0, i.e., 2*x* – 3*y* = 6.

Case II: *a *= –2 and *b* = 3

In this case, the equation of the line is 3*x* – 2*y* + 6 = 0, i.e., –3*x* + 2*y* = 6.

Thus, the required equation of the lines are 2*x* – 3*y* = 6 and –3*x* + 2*y* = 6.