Find the Standard Form of the Equation of the Ellipse $\frac { ( x + 6 ) ^ { 2 } } { 9 } + \frac { ( y + 9 ) ^ { 2 } } { 64 } = 1$

question 257

Multiple Choice

Find the standard form of the equation of the ellipse with the given characteristics.
Vertices: (6,1) , (6,17) , minor axis of length 3

• A) \(\frac { ( x + 6 ) ^ { 2 } } { 9 } + \frac { ( y + 9 ) ^ { 2 } } { 64 } = 1\)
• B) \(\frac { ( x - 6 ) ^ { 2 } } { 9 } + \frac { ( y - 9 ) ^ { 2 } } { 64 } = 1\)
• C) \(\frac { ( x - 6 ) ^ { 2 } } { 64 } + \frac { ( y - 9 ) ^ { 2 } } { 9 } = 1\)
• D) \(\frac { ( x - 9 ) ^ { 2 } } { 64 } + \frac { ( y - 6 ) ^ { 2 } } { 9 } = 1\)
• E) \(\frac { ( x + 9 ) ^ { 2 } } { 64 } + \frac { ( y + 6 ) ^ { 2 } } { 9 } = 1\)

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Definitions:

Categories

Distinct groups or classes into which items or individuals can be sorted based on shared qualities or characteristics.

Proportion

A statistical measure that indicates the fraction of the total population that possesses a particular attribute or characteristic.

Chi-squared Goodness-of-fit Test

This test assesses if observed frequencies in a single categorical variable match expected frequencies determined from a theoretical distribution.

Multinomial Distribution

A generalization of the binomial distribution, which deals with outcomes of a experiment that can fall into more than two categories.