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Question
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
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Solution
Let a and b be the intercepts made on the axes by the line passing through P(2, 2).
equation of line in intercept form
`"x"/"a" + "y"/"b" = 1`
This line passes through P(2, 2).
∴ `2/"a" + 2/"b" = 1` ..........(i)
It is given that the sum of the segments is 9.
∴ a + b = 9
b = 9 – a
Putting the value of b in (i),
`2/"a" + 2/(9 -"a") = 1`
or 2(9 – a) + 2a = a (9 – a)
18 – 2a + 2a = 9a – a2
or a2 – 9a + 18 = 0
or (a – 6)(a – 3) = 0
a = 6, 3
b = 3, 6
When a = 6 and b = 3, then the required equation of the line is
`"x"/6 + "y"/3 = 1`
or 3x + 6y = 18
or x + 2y = 6
When a = 3 and b = 6, then the required equation of the line is,
`"x"/3 + "y"/6 = 1`
2x + y - 6 = 0
or x + 2y - 6 = 0
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