If the portion of a line intercepted between the coordinates axes is divided by the point (2,-1) in the ratio of 3: 2 , then the equation of that line is

Step-by-step solution

Let the equation of the line be x a + y b =1 The line meets the coordinate axes at A(a, 0) and B(0, b) respectively. The coordinate of the point which divides the line joining A(a, 0) and B(0, b) in the ratio 3: 2 are ( 3 0+2 a 3+2 , 3 b+2 0 3+2 ) ( 2 a 5 , 3 b 5 ) If is given that, the point (2,-1) divides the A B in the ratio 3: 2 . 2 a 5 =2 and 3 b 5 =-1 a=5 and b= -5 3 Hence, the required equation of the required line is array rlrl & & x 5 + y -5 3 & =1 & x 5 - 3 y 5 & =1 & x-3 y & =5 & x-3 y-5 & =0 array