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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 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
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