Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Explanation

Let equation of line is
`(x)/(a)+(y)/(b)=1`…..`(1)`
This line passes through the point `(2,2)`
`:.(2)/(a)+(2)/(b)=1`……`(2`
Given, `a+b=9`
`implies a=9-b`………`(3)`
From equation `(2)`,
`(2)/(9-b)+(2)/(b)=1`
`implies(2b+18-2b)/((9-b)b)=1`
`implies18=9b-b^(2)`
`implies b^(2)-9b+18=0`
`implies (b-3)(b-6)=0`
`implies b=3` or `b=6`
If `b=3` then `a=9-3=6`
`:.` Equation of line is
`(x)/(6)+(y)/(3)=1impliesx+2y=6`
If `b=6` then `a=9-6=3`
`:.` Equation of line is
`(x)/(3)+(y)/(6)=1implies2x+y=6`