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The equation of the line, when the porti...

The equation of the line, when the portion of it intercepted between the axes is divided by the point (2, 3) in the ratio of 3 : 2, is

A

Either `x+y or 9x+y=12`

B

Either `x+y=5 or 4x+9y=30`

C

Either `x+y=4 or x+9y=12`

D

Either `x+y=5 or 9x+4y=30`

Text Solution

Verified by Experts

The correct Answer is:
D
Intercept form of line is `x/a+y/b=1`.
We know, the point which divides a line joining two points `(x_(1), y_(1))` and `(x_(2), y_(2))` in the ratio `m : n` is

`((mx_(2)+nx_(1))/(m+n), (my_(2)+ny_(1))/(m+n))`
Case 1 : `m : n =2 : 3`
`:. (2, 3)=(((2)(a)+3(0))/(2+3), (2(0)+3(b))/(2+3))`
`implies (2, 3)=((2a)/5, (3b)/5)`
`implies (2a)/5=2 , (3b)/5=3`
`implies a=5, b=5`.
`:.` Equation of line is `x/5+y/5=1 implies x+y=5`
Case 2 : `m : n =3 : 2`
`:. (2, 3)=((3(a)+2(0))/(3+2), (3(0)+2(b))/(3+2))`
`implies (2, 3) =((3a)/5, (2b)/5)`
`implies (3a)/5=2, (2b)/5=3`
`implies a=10/3, b=15/2`
`:.` Equation of line is `x/(10/3)+y/(15/2)=1`
`implies (3x)/10+(2y)/15=1`
`implies 9x+4y=30`
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