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

Question 119

Multiple Choice

Rotate the axes to eliminate the xyx y -term in the following equation.
30x2+203xy10y220x203y=0- 30 x ^ { 2 } + 20 \sqrt { 3 } x y - 10 y ^ { 2 } - 20 x - 20 \sqrt { 3 } y = 0


A) (y) 2+x=0\left( y ^ { \prime } \right) ^ { 2 } + x ^ { \prime } = 0
B) 103(y) 2103x=0- 10 \sqrt { 3 } \left( y ^ { \prime } \right) ^ { 2 } - 10 \sqrt { 3 } x ^ { \prime } = 0
C) 10(x) 2+10y=0- 10 \left( x ^ { \prime } \right) ^ { 2 } + 10 y ^ { \prime } = 0
D) (y) 210x10=0- \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 10 } - \frac { x ^ { \prime } } { 10 } = 0
E) (x) 220y20=0- \frac { \left( x ^ { \prime } \right) ^ { 2 } } { 20 } - \frac { y ^ { \prime } } { 20 } = 0

Correct Answer:

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