Write the Equation of the Ellipse in Standard Form $$25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$$

question 73

Multiple Choice

Write the equation of the ellipse in standard form. Identify the vertices and foci.
- $$25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$$

• A) \(x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( 0 , - 12 ) , ( 0 , - 2 )\)
• foci \(( 0 , - 7 - 2 \sqrt { 6 } ) , ( 0 , - 7 + 2 \sqrt { 6 } )\)
• B) \(x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( - 12,0 ) , ( - 2,0 )\)
• foci \(( - 7 - 2 \sqrt { 6 } , 0 ) , ( - 7 + 2 \sqrt { 6 } , 0 )\)
• C) \(x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( 2,0 ) , ( 12,0 )\)
• foci \(( 7 - 2 \sqrt { 6 } , 0 ) , ( 7 + 2 \sqrt { 6 } , 0 )\)
• D) \(x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( 0,2 ) , ( 0,12 )\)
• foci \(( 0,7 - 2 \sqrt { 6 } ) , ( 0,7 + 2 \sqrt { 6 } )\)

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Definitions:

Direct Labor-Hours

The total number of hours worked by employees directly involved in the manufacturing process.

Direct Materials Cost

The cost of raw materials that can be directly attributed to the production of a finished good.

Activity-Based Costing

A costing methodology that assigns overhead and indirect costs to specific products or activities based on their consumption of resources.

Direct Labor-Hours

The total hours worked by employees directly involved in the production of goods.