Find an Equation of the Hyperbola Centered at the Origin $\frac { 7 } { 4 }$

question 51

Multiple Choice

Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0) , asymptotes: y = ± $\frac { 7 } { 4 }$ x

• A) \(\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1\)
• B) \(\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 16 } = 1\)
• C) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1\)
• D) \(\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1\)

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Definitions:

Phase Transitions

The process of changing from one state of matter (solid, liquid, gas) to another, such as melting, freezing, vaporization, or condensation.

Branched Isomers

Molecules that have the same molecular formula but differ in the arrangement of their atoms due to branching in their structures.

Cyclohexane

Cyclohexane is a cycloalkane with the molecular formula C6H12, consisting of a ring of six carbon atoms, and is used as a solvent and in the synthesis of nylon.

Hexane

A hydrocarbon with the formula C6H14, commonly used as a non-polar solvent in the extraction of oils and fats.