If $f ( x , y ) = x ^ { 2 } + 6 y ^ { 2 }$

Multiple Choice

If $f ( x , y ) = x ^ { 2 } + 6 y ^ { 2 }$ , use the gradient vector $\nabla f ( 10,2 )$ to find the tangent line to the level curve $f ( x , y ) = 124$ at the point $( 10,2 )$ .
Select the correct answer.

A) $100 x + 36 y = 124$
B) $100 x - 124 y = 12$
C) $10 x + 12 y = 124$
D) $10 x + 12 y = 12$
E) $100 x - 12 y = 12$