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