Rotate the Axes So That the New Equation Contains No $\mathrm { xy } + 16 = 0$

question 145

Multiple Choice

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati
- $\mathrm { xy } + 16 = 0$

• A) \(\theta = 45 ^ { \circ }\)
• \(\frac { y ^ { \prime 2 } } { 32 } + \frac { x ^ { \prime 2 } } { 32 } = 1\)
• ellipse
• center at \(( 0,0 )\)
• major axis is \(y ^ { \prime }\)-axis
• vertices at \(( 0 , \pm 4 \sqrt { 2 } )\)
• B) \(\theta = 45 ^ { \circ }\)
• \(\frac { y ^ { \prime 2 } } { 32 } - \frac { x ^ { \prime 2 } } { 32 } = 1\)
• hyperbola
• center at \(( 0,0 )\)
• transverse axis is \(y ^ { \prime }\)-axis
• vertices at \(( 0 , \pm 4 \sqrt { 2 } )\)
• C) \(\theta = 45 ^ { \circ }\)
• \(y ^ { \prime 2 } = - 32 x ^ { \prime }\)
• parabola
• vertex at \(( 0,0 )\)
• focus at \(( - 8,0 )\)
• D) \(\theta = 36.9 ^ { \circ }\)
• \(\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 2 } = 1\)
• ellipse
• center at \(( 0,0 )\)
• major axis is the \(x ^ { \prime }\)-axis
• vertices at \(( \pm 2,0 )\)

Understand the distinctions between dependent and independent variables in experimental research.

Understand the concept of random selection and its importance in research.

Identify and explain different types of correlations between variables.

Recognize the importance of blinding participants in an experiment to prevent bias.

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