Solve the Problem $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 16 } = 1$

question 248

Multiple Choice

Solve the problem.
-The ellipse $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 16 } = 1$ is shifted down 3 units and right 8 units. Find an equation for the new ellipse and find the new center.

• A) \(\frac { ( x + 3 ) ^ { 2 } } { 5 } + \frac { ( y - 8 ) ^ { 2 } } { 11 } = 1\); center: \(( 3 , - 8 )\)
• B) \(\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 8 ) ^ { 2 } } { 11 } = 1\); center: \(( - 3,8 )\)
• C) \(\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1 ;\) center: \(( 8 , - 3 )\)
• D) \(\frac { ( x + 8 ) ^ { 2 } } { 5 } + \frac { ( y - 3 ) ^ { 2 } } { 11 } = 1\); center: \(( 8 , - 3 )\)

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Definitions:

Returns

The profit or loss derived from investing in or owning an asset over a given period.

Standard Deviation

A statistical measure that represents the dispersion or variation of a set of values, commonly used to assess risk in finance.

Average Return

Average return refers to the mean amount of profit or loss generated by an investment over a specified period.

Standard Deviation

A measure of the dispersion or variance in a distribution of data points, indicating how spread out the data is from its mean.