Find the Standard Form of the Equation of the Hyperbola $( \pm 5,0 ) \quad$

question 71

Multiple Choice

Find the standard form of the equation of the hyperbola with the given characteristics.
foci: $( \pm 5,0 ) \quad$ asymptotes: $y = \pm 3 x$

• A) \(\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1\)
• B) \(\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1\)
• C) \(\frac { y ^ { 2 } } { \frac { 5 } { 2 } } - \frac { x ^ { 2 } } { \frac { 45 } { 2 } } = 1\)
• D) \(\frac { x ^ { 2 } } { \frac { 5 } { 2 } } - \frac { y ^ { 2 } } { \frac { 45 } { 2 } } = 1\)
• E) \(\frac { x ^ { 2 } } { \frac { 45 } { 2 } } - \frac { y ^ { 2 } } { \frac { 5 } { 2 } } = 1\)

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Definitions:

Probability Density Function

A function that describes the likelihood of obtaining the possible values that a random variable can assume, used in continuous probability distributions.

Finite Population Correction Factor

A correction applied to standard errors or variances when sampling from a finite population without replacement, to account for the decreased variability.

Population Mean

The average of all the values in a population, calculated as the sum of all values divided by the number of values.

Sample Mean

The arithmetic average of a set of numerical values, calculated by adding them together and dividing by the number of observations.