The symmetric equations of the normal line to the surface $16 z = 4 x ^ { 2 } + y ^ { 2 }$ at (2, 4, 2) are

A) $\frac { x - 2 } { 4 } = y - 4 = \frac { z - 2 } { - 2 }$
B) $\frac { x - 2 } { 2 } = y - 4 = \frac { z - 2 } { - 4 }$
C) $\frac { x - 2 } { 2 } = y - 4 = \frac { z - 2 } { - 2 }$
D) $\frac { x - 2 } { 2 } = y - 4 = \frac { z - 2 } { 2 }$
E) $\frac { x - 2 } { - 2 } = y - 4 = \frac { z - 2 } { - 2 }$

Question

The symmetric equations of the normal line to the surface $16 z = 4 x ^ { 2 } + y ^ { 2 }$ at (2, 4, 2) are

A) $\frac { x - 2 } { 4 } = y - 4 = \frac { z - 2 } { - 2 }$
B) $\frac { x - 2 } { 2 } = y - 4 = \frac { z - 2 } { - 4 }$
C) $\frac { x - 2 } { 2 } = y - 4 = \frac { z - 2 } { - 2 }$
D) $\frac { x - 2 } { 2 } = y - 4 = \frac { z - 2 } { 2 }$
E) $\frac { x - 2 } { - 2 } = y - 4 = \frac { z - 2 } { - 2 }$

Quizplus · Accepted Answer

The normal vector to the surface is $\nabla f(2, 4, 2) = 8i + 4j - 16k$. So, the symmetric equations of the normal line are $\frac{x - 2}{8} = \frac{y - 4}{4} = \frac{z - 2}{-16}$.

The Symmetric Equations of the Normal Line to the Surface 16z=4x2+y216 z = 4 x ^ { 2 } + y ^ { 2 }16z=4x2+y2

The Symmetric Equations of the Normal Line to the Surface $16 z = 4 x ^ { 2 } + y ^ { 2 }$