Complete the Square to Determine the Type of Curve Represented $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

question 99

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

• A) \(( x + 2 ) ^ { 2 } = 9 ( y - 3 )\)
• , parabola
• B) \(\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1\)
• , ellipse
• C) \(\frac { ( x + 2 ) ^ { 2 } } { 8 } - \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1\)
• , hyperbola
• D) \(\frac { ( x + 3 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 3 } = 1\)
• , hyperbola
• E) none of these

Analyze and compare inflation rates over time using compound interest principles.

Evaluate the growth of financial figures over time under compounding interest to assess financial decisions.

Calculate the real rate of return on an investment taking inflation into account.

Understand and calculate effective interest rates for various compounding periods.

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