A straight line x a - y b =1 passes through the point (8,6) and cuts a triangle of area 12 sq units from the axes of coordinates. The equations of the straight lines are

Step-by-step solution

A straight line x a - y b =1 passes thought (8,6) . Then, 8 a - 6 b =1...(i) Area of triangle formed by axis and line =12 sq unit aligned & Area of triangle = 1 2 base height & aligned 12 & = 1 2 |(a) (-b)| 24=|-a b| |a b|=24, a b & = 24, b= 24 a aligned aligned Now, in Eq. (i) put b=24 / a array rlrl & & 8 a - 6 b & =1 & & 8 a - 6 24 a & =1 8 a - a 4 =1 & & 32-a^2 4 a & =1 32-a^2=4 a & a^2+4 a-32 & =0 (a+8)(a-4)=0 & a=-8 a & =4 & b=-3 b & =6 array Equation of lines are array c|l x -8 - y -3 =1 & x 4 - y 6 =1 -3 x+