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Question
Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3:10
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Solution
Let the line divide the coordinate axis in the ratio 3 : 10.
∴ x-intercept = 3k
y-intercept = 10k
∴ The equation of the straight line is `x/(3"k") + y/(10"k")` = 1
This line passes through the point P(1, 5).
∴ `1/(3"k") + 5/(10"k")` = 1
`1/(3"k") + 1/(2"k")` = 1
`(2"k"+ 3 "k")/(2"k" xx 3"k")` = 1
`(5"k")/(2"k" xx 3"k")` = 1
`5/(6"k")` = 1
⇒ k = `5/6`
∴ The required equation is
`x/(3(5/6)) + y/(10(5/6))` = 1
`x/(5/2) + y/(25/3)` = 1
`(2x)/5 + (3y)/25` = 1
`(10x + 3y)/25` = 1
10x + 3y = 25
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