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

The equation of a line in the intercept form is
`(x)/(a) + (y)/(b) = 1`
This line passes through (2,2). Therefore,
`(2)/(a) + (2)/(b) = 1 " " (1)`
It is given that a+b = 9, i.e.,
`b=9-a " " (2)` From (1) and (2), we get
`(2)/(a) + (2)/(9-a)= 1`
` " or " a^(2)-9a+18 = 0`
or (a-6)(a-3) = 0
i.e., a =6 or a= 3
If a = 6 and b=9-6 =3, then the equation of the line is
`(x)/(6) + (y)/(3) = 1 or x+2y-6 = 0`
If a = 3 and b =9-3 = 6, then the equation of the line is
`(x)/(3) + (y)/(6) = 1 or 2x+y-6 = 0`