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Multivariable Calculus

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Find the Equation of the Plane Tangent to the Surface S

MVCALC-EX0NZV

Let $S = \{ (x,y,z) \in \mathbb{R} | x^2 + y^2 + z^2 = 16 \; \text{and} \; x^2+y^2 \geq 4 \}$. Find the equation of the plane tangent to the surface $S$ at the point $P = (\sqrt{6}, \sqrt{6}, 2)$.

A

$6\sqrt2x+6\sqrt2y+4\sqrt3z = 24\sqrt3+4\sqrt6$

B

$6\sqrt3x+6\sqrt3y+4\sqrt2z = 44\sqrt2$

C

$\sqrt6x+\sqrt6y+2z = 0$

D

$x+y+z = 24\sqrt3+4\sqrt6$

E

None of the Above