differential geometry – Curvature of elliptical helix curve

Consider the following helix curve: $beta(t)=(ae^{bt} cos t, ae^{bt} sin t,ct) $

Now show that the curvature of this curve is a constant if and only if $a^2=b^2$

What I think:

Simply compute the curvature of the curve and use the condition $a^2=b^2$ to show that curvature is a constant.