Show that the curve

$\displaystyle r(t)=t^2\mathbf{i}+t\mathbf{j}+(5t-4)\mathbf{k}$ is normal to the surface $\displaystyle 2x^2+y^2+5z^2=8$ at the point $\displaystyle (1,1,1)$

Would I start off by finding the tangent to the surface, and then showing that the vector given by the curve is normal to the tangent plane?