# Geodesic of a Surface in $\mathbb{R}^3$

I'm not familiar with geodesics. How can I show that a curve $c$ given by $c(t)=(t,f(t)\cos{\alpha},f(t)\sin{\alpha})$ for $\alpha$ constant is a geodesic on $M$ where $M=\left\{(x,y,z) \in \Bbb{R}^3 \mid f(x)=y^2+z^2\right\}$?

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Clairaut's relation. en.wikipedia.org/wiki/Clairaut%27s_relation –  Will Jagy Feb 12 '13 at 20:36
Also, meridians on a surface of revolution are always geodesics, and your notation is poor. –  Will Jagy Feb 12 '13 at 20:44