For the vector field $F$ and curve C $,$ complete the following.

a$.$ Determine the points $($if any$)$ on the curve $C$ at which the vector field $F$ is tangent to $C.$

b$.$ Determine the points $($if any$)$ on the curve $C$ at which the vector field $F$ is normal to $C.$

c$.$ Sketch $C$ and a few representative vectors of $F$ on $C.$

$F=($:$\frac{1}{2},0$:$),$ where $C=\{(x,y)$:$y-3x^2=1\}$

a$.$ Where is F tangent to C$?$ Select the correct choice below and fill in any answer boxes within your choice.

A$.F$ is tangent to $C$ at $(0,1).$

$($Type an ordered pair. Use a comma to separate answers as needed.$)$

B$.$ There are no points where $F$ is tangent to $C.$

C$.F$ is tangent to $C$ at every point on $C.$

b$.$ Where is F normal to C $?$ Select the correct choice below and fill in any arswer boxes within your choice.

A$.F$ is orthogonal to the tangent vector of $C$ at $.$

$($Type an ordered pair. Use a comma to separate answers as needed.$)$

B$.$ There are no points where $F$ is normal to $C.$

C$.F$ is normal to $C$ at every point on $C.$