Find the Vertices and Foci of the Hyperbola $$\frac { ( x + 5 ) ^ { 2 } } { 64 } - \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$$

question 55

Multiple Choice

Find the vertices and foci of the hyperbola.
- $$\frac { ( x + 5 ) ^ { 2 } } { 64 } - \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$$

• A) Vertices: \(( 3,3 ) , ( 3 , - 13 )\); Foci: \(( 3 , - 15 ) , ( 3,5 )\)
• B) Vertices: \(( 3,1 ) , ( 3 , - 11 )\); Foci: \(( 3 , - 11 ) , ( 3,1 )\)
• C) Vertices: \(( 1,3 ) , ( - 11,3 )\); Foci: \(( - 11,3 ) , ( 1,3 )\)
• D) Vertices: \(( 3,3 ) , ( - 13,3 )\); Foci: \(( - 15,3 ) , ( 5,3 )\)

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Definitions:

Meso

Refers to a stereochemical term describing a compound with multiple stereocenters that is superposable on its mirror image, often due to an internal plane of symmetry, thus not being chiral.

Asymmetric Carbons

Carbon atoms bonded to four different atoms or groups, leading to chirality or mirror-image isomerism.

Stereochemistry

The study of the spatial arrangement of atoms in molecules and its influence on the chemical and physical properties of substances.

Stereochemistry

The study of the three-dimensional structures of molecules, focusing on the spatial arrangement of atoms and the implications for the chemical behavior of the compounds.