Find equations for $($a$)$ the tangent plane and $($b$)$ the normal line at the point $P_0(3,2,2)$ on the surface $4x^2+3y^2+z^2=52.$

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

A$.2x+3y+z=14$

B$.14x+3y+2z=52$

C$.6x+3y+z=26$

D$.6x+2y+z=24$

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

A$.x=3-24t$ B$.$

$x=24+3t$

$y=12+2t$

$z=4+2t$

$y=2+12t$

$z=2-4t$

C$.$

$x=3+24t$

$y=2+12t$

$z=2+4t$

D$.$

$x=2+4t$

$y=2-12t$

$z=3+24t$