Question 106
In the Cartesian plane, two graphs $\Gamma_1$ and $\Gamma_2$ of monic quadratic trinomials and two non-parallel lines $l_1$ and $l_2$ are drawn. Assume that $\Gamma_1$ and $\Gamma_2$ cut out segments of equal lengths on $l_1$, and that they cut out segments of equal lengths on $l_2$. Prove that $\Gamma_1$ and $\Gamma_2$ coincide.