Rotate the Axes So That the New Equation Contains No $24 x y - 7 y ^ { 2 } + 36 = 0$

question 186

Multiple Choice

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati
- $24 x y - 7 y ^ { 2 } + 36 = 0$

• A) \(\theta = 36.9 ^ { \circ }\)
• \(\frac { y ^ { \prime 2 } } { 9 } - \frac { x ^ { \prime 2 } } { 16 } = 1\)
• hyperbola
• \(\text { center at }(0,0)\)
• transverse axis is the \(y ^ { \prime }\)-axis
• \(\text { vertices at }(0, \pm 3)\)
• B) \(\theta = 36.9 ^ { \circ }\)
• \(\frac { 4 y ^ { \prime 2 } } { 9 } - \frac { x ^ { \prime 2 } } { 4 } = 1\)
• hyperbola
• \(\text { center at }(0,0)\)
• transverse axis is the \(y ^ { \prime }\)-axis
• vertices at \(\left( 0 , \pm \frac { 3 } { 2 } \right)\)
• C) \(\theta = 36.9 ^ { \circ }\)
• \(\frac { y ^ { \prime 2 } } { 4 } - \frac { 4 x ^ { \prime 2 } } { 9 } = 1\)
• hyperbola
• center at \(( 0,0 )\)
• transverse axis is the \(y ^ { \prime }\)-axis
• vertices at \(( 0 , \pm 2 )\)
• D) \(\theta = 53.1 ^ { \circ }\)
• \(\frac { y ^ { \prime 2 } } { 4 } - \frac { 4 x ^ { \prime 2 } } { 9 } = 1\)
• hyperbola
• center at \(( 0,0 )\)
• transverse axis is the \(y ^ { \prime }\)-axis
• vertices at \(( 0 , \pm 2 )\)

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