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

question 16

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

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Definitions:

Barriers

Refers to obstacles or impediments that hinder progress or the achievement of an objective.

Unique Characteristics

Distinctive attributes or features that set something apart from similar entities.

Rent Controls

are government policies or laws that limit the amount landlords can charge for leasing properties to protect tenants from rapid increases in rent.

Equilibrium Price

The market price at which the quantity of goods supplied is equal to the quantity of goods demanded.