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:

Collar Bone

The clavicle, a long bone that serves as a strut between the shoulder blade and the sternum or breastbone, part of the human skeletal system.

Clavicle

The collar bone, articulating with the sternum and scapula.

Subluxation

The partial dislocation or misalignment of a joint or organ.

Articulating Surfaces

The contact regions between bones that move against each other in a joint, usually covered with articular cartilage.