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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.

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Solution

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

It is given that,
a+b= 1....(1)
and ab=6....(2)

On solving equation (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 xa+yb=1 or bx+ayab=0.

case1: a=3 and b=2
In this case the equation of the line is 2x+3y+6=02x3y=6

case2: a=2 and b=3
In this case the equation of line is 3x2y+6=03x+2y=6

Thus, the required equation of the lines are 2x3y=6 and 3x+2y=6.

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