Find the Standard Form of the Equation of the Ellipse $( - 6,4 )$

question 217

Multiple Choice

Find the standard form of the equation of the ellipse with the given characteristics.
Center: $( - 6,4 )$ , a = 5c, foci: $( - 8,4 ) , ( - 4,4 )$ , where a - thr semimajor axis, b - semiminor axis and $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ .

• A) \(\frac { ( x - 6 ) ^ { 2 } } { 96 } + \frac { ( y + 4 ) ^ { 2 } } { 100 } = 1\)
• B) \(\frac { ( x + 6 ) ^ { 2 } } { 96 } + \frac { ( y - 4 ) ^ { 2 } } { 100 } = 1\)
• C) \(\frac { ( x + 6 ) ^ { 2 } } { 100 } + \frac { ( y - 4 ) ^ { 2 } } { 96 } = 1\)
• D) \(\frac { ( x - 4 ) ^ { 2 } } { 100 } + \frac { ( y + 6 ) ^ { 2 } } { 96 } = 1\)
• E) \(\frac { ( x + 4 ) ^ { 2 } } { 100 } + \frac { ( y - 6 ) ^ { 2 } } { 96 } = 1\)

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Definitions:

Atomic Sentences

Simple statements in logic that cannot be broken down further into smaller statements.

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The valuation of statements as true or false in logic.

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A table used in logic to determine whether a compound statement is true or false under all possible situations.

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A type of sentence that contains no logical connectors and represents the simplest form of statement that can be either true or false.