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

question 58

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the following equation and then write the equation in standard form.
$$3 x ^ { 2 } - 12 x y + 12 y ^ { 2 } + 15 \sqrt { 5 } y + 3 = 0$$

• A) \(\left( x ^ { \prime } - 1 \right) ^ { 2 } = 3 \left( y ^ { \prime } - \frac { 4 } { 5 } \right)\)
• B) \(\left( x ^ { \prime } + 3 \right) ^ { 2 } = - 5 \left( y ^ { \prime } + \frac { 1 } { 3 } \right)\)
• C) \(\left( y ^ { \prime } + 1 \right) ^ { 2 } = - \left( x ^ { \prime } - \frac { 4 } { 5 } \right)\)
• D) \(\left( y ^ { \prime } - \frac { 4 } { 5 } \right) ^ { 2 } = 3 \left( x ^ { \prime } - 1 \right)\)
• E) \(\left( y ^ { \prime } + \frac { 4 } { 5 } \right) ^ { 2 } = x ^ { \prime } + \frac { 1 } { 3 }\)