Find the Standard Form of the Equation of the Ellipse $$2 x ^ { 2 } + 8 y ^ { 2 } + 24 x - 64 y + 16 = 0$$

question 23

Multiple Choice

Find the standard form of the equation of the ellipse below.
$$2 x ^ { 2 } + 8 y ^ { 2 } + 24 x - 64 y + 16 = 0$$

• A) \(\frac { ( x - 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } + \frac { ( y + 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } = 1\)
• B) \(\frac { ( x + 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } + \frac { ( y - 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } = 1\)
• C) \(\frac { ( x + 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } - \frac { ( y - 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } = 1\)
• D) \(\frac { ( x - 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } + \frac { ( y + 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } = 1\)
• E) \(\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } - \frac { ( y + 6 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } = 1\)

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Definitions:

Production Increase

A situation where a company enhances its output of products due to higher demand, improved efficiencies, or expansion efforts.

Income Change

A variation in an individual's or organization's income level due to factors such as economic conditions, employment status changes, or business profitability adjustments.

Variable Costing

Variable costing is an accounting method that only considers variable costs (costs that change with production levels) when calculating the cost of goods sold or produced.