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

Solving the equations of the sides taken in pairs, we obtain that the coordinates of the vertices A, B, C, D of theparallelogram ABCD are A (2, 1), B ( 3, 1), C ( 3, 5), D (2, 5)respectively. Hence, the equations of diagonals AC and BD are4x−y−7=0 and 4x+y−13=0.