Find Equations for the Tangent Plane and the Normal Line $x ^ { 2 } + 3 y ^ { 2 } + 9 z ^ { 2 } = 16$

question 118

Multiple Choice

Find equations for the tangent plane and the normal line to the surface with equation $x ^ { 2 } + 3 y ^ { 2 } + 9 z ^ { 2 } = 16$ at the point $P ( 2,1,1 )$

• A) \(x + 3 y + 9 z = 16\) , \(\frac { x - 2 } { 2 } = y - 3 = z - 9\)
• B) \(2 x + 3 y + 9 z = 16\) , \(\frac { x - 2 } { 2 } = \frac { y - 1 } { 3 } = \frac { z - 1 } { 9 }\)
• C) \(x + 3 y + 9 z = 16\) , \(\frac { x - 2 } { 2 } = \frac { y - 1 } { 3 } = \frac { z - 1 } { 9 }\)
• D) \(2 x + 3 y + 9 z = 16\) , \(\frac { x - 2 } { 2 } = y - 3 = z - 9\)

---

Definitions:

Generation

A group of individuals born and living at about the same time, regarded collectively.

Lifespan Human Development

The study of how people grow, change, and stay the same throughout their entire life, from conception to death.

Ethical Considerations

The reflections and evaluations of moral principles and standards that guide actions and decisions, especially in professional practices.

Research Study

A systematic investigation designed to develop or contribute to generalizable knowledge through the collection and analysis of data.