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

question 12

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:

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A waste product formed from the breakdown of purines in the body, which is excreted in urine. High levels may lead to gout or kidney stones.

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Nitrogenous Wastes

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