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