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

---

Definitions:

R Groups

The variable side chain attached to the alpha carbon of an amino acid that determines the amino acid's properties and its role in protein structure and function.

Peptide Bond

A distinctive covalent carbon-to-nitrogen bond that links amino acids in peptides and proteins.

Condensation Reaction

A chemical reaction where two molecules combine to form a single molecule, releasing a small molecule as a byproduct, such as water.

Polypeptide Chain

A linear organic polymer consisting of a large number of amino-acid residues bonded together in a chain, forming part of (or the whole of) a protein molecule.