Question

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

Answer 1

Let the segments cut on the axes be a and b.

Given: a + b = 1, ab = –6

b = 1 – a

∴ a(1 – a) = –6

or a – a₂ = –6

a₂ – a – 6 = 0

or (a – 3) (a + 2) = 0

∴ a = 3, –2

∴ b = –2, 3

3, equation of line with –2 intercept,

`"x"/3 + "y"/(-2) = 1`

or 2x – 3y = 6

And equation of line with -2, 3 intercepts,

`"x"/(-2) + "y"/3 = 1`

or –3x + 2y = 6