If $f ( x , y ) = x ^ { 2 } + 9 y ^ { 2 }$

Multiple Choice

If $f ( x , y ) = x ^ { 2 } + 9 y ^ { 2 }$ , use the gradient vector $\nabla f ( 10,2 )$ to find the tangent line to the level curve $f ( x , y ) = 136$ at the point $( 10,2 )$ . Select the correct answer.

A) $100 x + 81 y = 136$
B) $100 x - 136 y = 12$
C) $10 x + 18 y = 136$
D) $100 x - 18 y = 12$
E) $10 x + 18 y = 12$