Convert the Equation to the Standard Form for a Hyperbola $$9 y ^ { 2 } - 4 x ^ { 2 } + 18 y + 16 x - 43 = 0$$

question 87

Multiple Choice

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
- $$9 y ^ { 2 } - 4 x ^ { 2 } + 18 y + 16 x - 43 = 0$$

• A) \(\frac { ( y + 1 ) ^ { 2 } } { 4 } - \frac { ( x - 2 ) ^ { 2 } } { 9 } = 1\)
• B) \(\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1\)
• C) \(\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1\)
• D) \(\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1\)

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Definitions:

Sudden

Occurring or done quickly and unexpectedly, without warning.

Emotional Regulation

The process of managing and responding to one's emotions in a healthy and productive manner.

Temperament

The inherent part of an individual's personality concerning their emotional nature and habitual behaviors.

Chess and Thomas

Researchers known for their contributions to developmental psychology, particularly in the study of temperament in children.