Rotate the Axes to Eliminate The $x y$ -Term in the Following Equation

question 49

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the following equation. $18 x ^ { 2 } - 12 \sqrt { 3 } x y + 6 y ^ { 2 } + 12 x + 12 \sqrt { 3 } y = 0$

• A) \(\left( y ^ { \prime } \right) ^ { 2 } + x ^ { \prime } = 0\)
• B) \(6 \sqrt { 3 } \left( y ^ { \prime } \right) ^ { 2 } + 6 \sqrt { 3 } x ^ { \prime } = 0\)
• C) \(6 \left( x ^ { \prime } \right) ^ { 2 } - 6 y ^ { \prime } = 0\)
• D) \(\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } + \frac { x ^ { \prime } } { 6 } = 0\)
• E) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } + \frac { y ^ { \prime } } { 12 } = 0\)

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Definitions:

Sympathetic Nervous System

A part of the autonomic nervous system that prepares the body for physical activity by increasing heart rate, dilating airways, and mobilizing energy stores, among other functions.

Parasympathetic Nervous System

The division of the autonomic nervous system that conserves energy and restores the body to a state of calm.

Fight-Or-Flight

A physiological response to perceived threats, preparing the body to fight or flee.

Rest And Digest

Describes the activity of the parasympathetic nervous system, promoting a state of calm and supporting digestive and recuperative processes.