Complete the Square to Determine the Type of Curve Represented $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

question 103

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

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

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Definitions:

Step-Growth Polymerization

A polymerization process in which bi-functional or multi-functional monomers react to form first dimers, then trimers, and so on, growing by stepwise addition.

Polyethylene

A versatile synthetic polymer made from the polymerization of ethylene, widely used in plastic bags, containers, and packaging.

Addition Polymer

A polymer formed by the successive addition of monomer molecules with unsaturated bonds, leading to a long chain molecule.

Condensation Polymer

A polymer formed by the reaction where two molecules combine with the simultaneous elimination of a small molecule, such as water.