The equations to a pair of opposite sides of parallelogram are x2-5x+6=0 and y2-6y+5=0, the equations to its diagonals are

x2-5x+6=0⇒x-2x-3=0⇒two of the parallel sides are x = 2, x = 3y2-6y+5=0⇒y-1y-5=0⇒other two parallel sides are y = 1, y = 5So, the vertices of the parallelogram are (2, 1), (2, 5), (3, 1), (3, 5). Equation of the diagonal are y−5=1−53−2(x−2)⇒4x + y = 13  andy−1=5−13−2(x-2)⇒y = 4x - 7