Q. 134.3( 86 Votes )

Find equati

Answer :

We know that equation of the line making intercepts a and b on x-and y-axis, respectively, is . … (1)


Given, sum of intercepts = 9


a + b = 9


b = 9 - a


Substituting b value in the above equation,



Given, the line passes through the point (2, 2),


So,





18 = a (9 a)


18 = 9a a2


a2 – 9a + 18 = 0


Factorizing,


a2 – 3a – 6a + 18 = 0


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


(a 3) (a 6) = 0


a = 3 or a = 6


Substituting in (1),


Case 1 (a = 3):


Then b = 9 – 3 = 6



2x + y = 6


2x + y 6 = 0


Case 2 (a = 6):


Then b = 9 – 6 = 3



x + 2y = 6


x + 2y 6 = 0


Ans. The equation of the line is 2x + y – 6 = 0 or x + 2y – 6 = 0.


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