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

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

It is given that

a + b = 1 ---------(1)

ab = -6 ---------(2)

On solveing equations (1) and (2), we get,

a = 3 and b = -2 or a = -2 and b = 3

We know that the equation of the line whose intercepts on the axes are a and b is

=> bx + ay – ab = 0

Now, when a = 3 and b = -2 , we get

The equation of the line is -2x + 3y + 6 = 0

=> 2x – 3y = 6

And when a = -2 and b = 3, we get,

The equation of the line is 3x – 2y +6 = 0

=> -3x + 2y = 6

Therefore, the equation of the lines are 2x – 3y = 6 or -3x + 2y = 6.