The equations of pairs of opposite sides of a parallelogram are x2−5x+6=0  and y2−6y+5=0 . The equations of its diagonals are

The two pairs are x2−5x+6=0  and y2−6y+5=0 . Hence, the sides of the parallelogram are , y=1 , x=3,y=5, , x=2 . The vertices, taken in order are A(2,1),B(3,1),C(3,5)  and D(2,5) . HenceThe two diagonals are (ACand  BD)         y−1=5−13−2(x−2)         y-1=4(x-2)And   y−1=5−12−3(x−3)y-1=4-1x-3i.e. 4x−y−7=0  and 4x+y−13=0 .