Complete the Square to Determine the Type of Curve Represented $x ^ { 2 } + 4 x - 8 y + 36 = 0$

question 42

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 4 x - 8 y + 36 = 0$

• A) \(( x + 2 ) ^ { 2 } = 8 ( y - 5 )\)
• , parabola
• B) \(\frac { ( x + 2 ) ^ { 2 } } { 8 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1\)
• , ellipse
• C) \(\frac { ( x + 2 ) ^ { 2 } } { 8 } - \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1\)
• , hyperbola
• D) \(( x + 2 ) ^ { 2 } = 4 ( y - 5 )\)
• , parabola
• E) none of these

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Definitions:

Make Goods

Products or services offered to compensate for a deficiency or to fulfill a previously unmet obligation.

Sell or Lease

The commercial decision to either transfer ownership of a property or product for a price or to grant its use to someone else under a rental agreement.

Liable

Legally responsible for one's actions or obligations, often in the context of paying damages or facing legal consequences.

Harm

Damage or injury to a person or property.