The equations to a pair of opposite sides of a parallelogram are $x^2-5x+6=0$ and $y^2-6y+5=0$. Find the equations of its diagonals

Question

Aside from solving this question, my main query is, how is such a situation even possible? The lines are parabolic, how can they ever be sides of a parallelogram?

Answer 1

$y=x^2−5x+6$ would be parabolic, but $x^2−5x+6=0$ means $x=2$ or $x=3$.

Perhaps this picture will help understanding:

Answer 2

If you factor the first, you get $(x-3)(x-2)=0$, which is a pair of vertical lines. It is not a parabola. If you factor the second, you get a pair of horizontal lines. That makes a rectangle.