## Parabola puzzle

Posted on: November 25th, 2014 by
Let $y=ax^2+b_1x+c_1$ and $y=ax^2+b_2x+c_2$ be two parabolas with the same coefficient for the $x^2$ term. The y-intercepts of the two parabolas are $(0,c_1)$ and $(0,c_2)$ respectively. Let the two parabolas intersect at $(x_1,y_1)$ and let the tangent to the two parabolas drawn at $(0,c_1)$ and $(0,c_2)$ intersect at $(x_2,y_2)$. Show using physics that $x_1=x_2$.