Find equations for $($a$)$ the tangent plane and $($b$)$ the normal line at the point $P_0(2,1,2)$ on the surface $x^2+4y^2+3z^2=20.$

$($a$)$ Which equation describes the tangent plane?

A$.x+2y+3z=10$

B$.3x+4y+5z=20$

C$.5x+4y+3z=20$

D$.x+5y+3z=13$

$($b$)$ Select the equations for the normal line.

A$.$

$x=2+4t$

$y=1+8t$

$z=2+12t$

B$.$

$x=2+12t$

$y=1-8t$

$z=2+4t$

C$.$

$x=2-4t$

$y=1+8t$

$z=2-12t$

D$.$

$x=4+2t$

$y=8+t$

$z=12+2t$