If the area of the triangle formed by the pair of lines 8 x^2-6 x y+y^2=0 and the line 2 x+3 y=a is 7 , then a is equal to

Step-by-step solution

Given pair of lines is 8 x^2-6 x y+y^2=0 . aligned & 8 ( x y )^2-6 ( x y )+1=0 & [4 ( x y )-1 ] [2 ( x y )-1 ]=0 & 4 x y =1 and 2 x y =1 & 4 x=y and 2 x=y & aligned Also, other line is 2 x+3 y=a On solving Eqs. (i) and (ii), we get O(0,0), A ( a 14 , 2 a 7 ) and B ( a 8 , a 4 ) array ll Area of A B C= 1 2 || array ccc 0 & 0 & 1 a 14 & 2 a 7 & 1 a 8 & a 4 & 1 array | & 7= 1 2 | ( a^2 56 - 2 a^2 56 ) | & 7= 1 2 | -a^2 56 | & 14 56=a^2 & a=28 array