Rotate the Axes So That the New Equation Contains No $$5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0$$

question 196

Multiple Choice

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati
- $$5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0$$

• A) \(\theta = 45 ^ { \circ }\)
• \(y ^ { \prime 2 } = - 4 x ^ { \prime }\)
• parabola
• vertex at \(( 0,0 )\)
• focus at \(( - 1,0 )\)
• B) \(\theta = 45 ^ { \circ }\)
• \(\frac { x ^ { \prime 2 } } { 4 } - y ^ { \prime 2 } = 1\)
• hyperbola
• center at \(( 0,0 )\)
• transverse axis is the \(x ^ { \prime }\)-axis
• vertices at \(( \pm 2,0 )\)
• C) \(\theta = 45 ^ { \circ }\)
• \(x^{\prime 2}=-4 y^{\prime}\)
• parabola
• vertex at \(( 0,0 )\)
• focus at \(( 0 , - 1 )\)
• D) \(\theta = 45 ^ { \circ }\)
• (\frac { x ^ { \prime 2 } } { 4 } + y ^ { \prime 2 } = 1\)
• ellipse
• center at \(( 0,0 )\)
• major axis is the \(x ^ { \prime }\)-axis
• vertices at \(( \pm 2,0 )\)

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