Angle between two parabolas I'm a little confused about a problem that asks me to find the angle between the two parabolas $$y^2=2px-p^2$$ and  $$y^2=p^2-2px$$ at their intersection. I used implicit differentiation to find the slopes $$y'=\frac{-p}{y}$$ and $$y'=\frac{p}{y}$$ Using the formula for the angle between two lines $\tan\alpha=|\frac{m_2-m_1}{1+m_2m_1}|$ with some substitutions I ended up with  $\tan\alpha=|\frac{y}{x}|$. When I set the two equations equal to one another to find the point of intersection I ended up with $x=0$ and $y=±p$. 
I know these values lead to tangent being undefined, can I infer from this fact that the angle between these parabolas is a right angle? The solution says that they intersect at right angles, but I'm confused about using something that is undefined to formulate my answer, if it turns out to be correct. Thanks for any help.

Ok, ok, let's don't divide by zero. Parametric equations of this curves are
$$
C1: \left(\frac{p^2 + y^2}{2p},\, y\right)\\
C2: \left(\frac{p^2 - y^2}{2p},\, y\right)
$$
($p\ne 0$, ok, right? :) Tangent vectors are
$$
C1: \left(\frac{y}{p},\, 1\right)\\
C2: \left(-\frac{y}{p},\, 1\right)
$$
At point of intersection ($y=0$) both are equal to $(0,\, 1)$, and angle is zero.
