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Find the equation of the lines which cut off intercepts on the axes whose sum and product are 2 and - 8 respectively.

Asked by Topperlearning User 30th April 2014, 8:22 AM
Answered by Expert
Answer:

Let a, b be the intercepts, the lines makes on the axes

Sum of intercepts = a + b = 2                                     ---(i)
Product of intercepts = ab = -8                                --- (ii)
From (i) and (ii),
a (2 - a) = -8
      2a - a2 = -8

        a2 - 2a - 8 = 0

        a2 -(4 - 2) a - 8 = 0
        (a - 4) (a + 2) = 0
         a - 4 = 0 or a + 2 = 0
       a = 4 or a = - 2
If a = 4, then
4 + b = 2
        b = - 2
And if a = - 2, then
            - 2 + b = 2
        b = 4.
Hence, equations of lines are
        x - 2y = 4  and - 2x + y = 4.
Answered by Expert 30th April 2014, 10:22 AM
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