A line cuts off on the coordinate axes positive intercepts whose sum is 4 . If it passes through ( 9 2 ,-5 ) , its equation is

Step-by-step solution

Let the equation of line be x a + y b =1 . Then a+b=4 aligned & array l x a + y 4-a =1 x(4-a)+y a array & a(4-a) aligned This passes through ( 9 2 ,-5 ) . array ll & 9 2 (4-a)-5 a=a(4-a) & 36-9 a-10 a=8 a-2 a^2 & 2 a^2-27 a+36=0 & a=12 or 3 2 but a 12 & a= 3 2 b= 5 2 array Required equation is array cc & 2 x 3 + 2 y 5 = 1 & 10 x+6 y=15 array