设曲面的参数方程为
$$
\left\{\begin{array}{l}
x=\sin \varphi \cos \theta \\
y=4 \sin \varphi \sin \theta,(0 \leq \varphi \leq \pi, 0 \leq \theta \leq 2 \pi) \\
z=4 \cos \varphi
\end{array}\right.
$$
求该曲面在 $\varphi=\frac{\pi}{4}, \theta=\frac{\pi}{4}$ 点处的切平面与法线方程.
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$
$\text{E.}$
$\text{F.}$