Q. 54.8( 11 Votes )

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

Answer :

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


Given : Let a and b be two intercepts of x-axis and y-axis respectively.


sum of the intercepts is 9,i.e,a+b = 9


a = 9 – b or b = 9 – a


Formula used:


The equation of a line is given by:


= 1


The given point (2, 2) passing through the line and satisfies the equation of the line.


= 1


2(9 – a) + 2a = 9a – a2


18 – 2a +2a = 9a – a2


a2 – 9a + 18 = 0


a2 – 6a – 3a + 18 =0


a(a - 6) - 3(a - 6) = 0


(a - 3) (a - 6) = 0


a = 3, a = 6


when a = 3, b=6 and a=6, b=3


case 1 : when a=3 and b=6


Equation of the line : = 1



Hence, 2x + y = 6 is the required equation of the line.


case 2 : when a=6 and b=3


Equation of the line : = 1


= 1


Hence , x + 2y = 6 is the required equation of the line.


Therefore, 2x + y = 6 is the required equation of the line when a=3 and b=6.And , x + 2y = 6 is the required equation of the line when a=6 and b=3.


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