Find the Equation of the Hyperbola with Center $( 3 , - 3 ) , a ^ { 2 } = 49$

question 53

Multiple Choice

Find the equation of the hyperbola with center $( 3 , - 3 ) , a ^ { 2 } = 49$ and $b ^ { 2 } = 25$ .

• A) \(\quad \frac { ( x - 3 ) ^ { 2 } } { 49 } - \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1\)
• B) \(\quad \frac { ( x - 3 ) ^ { 2 } } { 49 } - \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1\)
• C) \(\quad \frac { ( x + 3 ) ^ { 2 } } { 49 } - \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1\)
• D) \(\quad \frac { ( x - 3 ) ^ { 2 } } { 25 } - \frac { ( y + 3 ) ^ { 2 } } { 49 } = 1\)
• E) \(\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1\)

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Definitions:

Necessary Reagents

Chemical substances required to carry out a specific chemical reaction, often used to facilitate or enable transformations in organic synthesis.

Reaction

A process through which one or more substances are changed into one or more different substances, involving the rearrangement of atoms.

Major Organic Product

The leading output of an organic chemical reaction, characterized by its highest production level.

Structure

The arrangement and relations between parts or elements of something complex, often used to describe the molecular arrangement in chemistry.