If 2 x^2+3 x y-2 y^2=0 represents two sides of a parallelogram and 3 x+y+1=0 is one of its diagonals, then the other diagonal is

Step-by-step solution

As we know that, If the lines a x^2+2 h x y+b y^2=0 be two sides of a parallelogram and the line l x+m y=1 be one of its diagonals, then other diagonal is y(b l-h m)=x(a m-h l) Here, a=2, b=-2, h= 3 2 l=-3, m=-1 Putting all values in Eq. (i), we get aligned y (6+ 3 2 ) & =x (-2+ 9 2 ) y ( 15 2 ) & =x ( 5 2 ) 15 y & =5 x 3 y & =x x-3 y=0 aligned