Question

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

Answer 1

`x/a + y/b = 1`
given `a+b=9`
`b=9-a`
so `x/a + y/(9-a) = 1`
`2/a + 2/(9-a) = 1`
`2(9-a) + 2a = a(9-a)`
`18- 2a + 2a = 9a - a^2`
`a^2 - 9a + 18=0`
`(a-3)(a-6)=0`
`a=3 or 6`
when a=3`, b=9-3=6`
when a=6`, b=9-6=3`
so equations are
`x/3 + y/6 = 1`
`x/6 + y/3 = 1`
answer