If $f ( x , y ) = x ^ { 2 } + 7 y ^ { 2 }$

Multiple Choice

If $f ( x , y ) = x ^ { 2 } + 7 y ^ { 2 }$ use the gradient vector $\nabla f ( 10,2 )$ to find the tangent line to the level curve $f ( x , y ) = 136$ at the point $( 10,2 )$ .

A) $10 x + 14 y = 12$
B) $10 x + 14 y = 136$
C) $100 x - 49 y = 12$
D) $100 x + 49 y = 136$
E) $100 x - 14 y = 12$