JEE Advance - Mathematics (1994 - No. 30)
The equations to a pair of opposites sides of parallelogram are $${x^2} - 5x + 6 = 0$$ and $${y^2} - 6y + 5 = 0,$$ the equations to its diagonals are
$$x + 4y = 13,\,y = 4x - 7$$
$$4x + y = 13,\,4y = x - 7$$
$$4x + y = 13,\,y = 4x - 7$$
$$y - 4x = 13,\,y + 4x = 7$$