Let a line intersect the co-ordinate axes in points A and B such that the area of the triangle O A B is 12 sq. units. If the line passes through the point (2,3) , then the equation of the line is

Step-by-step solution

Area of A O B=12 sq. units array ll & 1 2 a b=12 & a b=24 & b= 24 a ...(i) array Equation of line in point slope form is aligned & y-a= -a b (x-0) & y-a= -a x 24 a aligned ...[from (i)] y- a = - a ^2 x 24 ...(ii) Since line passes through (2,3) aligned & 3-a= -a^2(2) 24 & 3-a= -a^2 12 & & a^2-12 a+36=0 & & (a-6)^2=0 & a=6 & & = 24 6 =4...[from(i)] aligned Required equation of line is aligned & y-6= -36 x 24 ...[from(ii)] & 2 y-12=-3 x & 3 x+2 y-12=0 & 3 x+2 y=12 aligned ...[from (ii)]