Find the Center, Foci, and Vertices of the Ellipse $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

question 3

Multiple Choice

Find the center, foci, and vertices of the ellipse.
- $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

• A) \(( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1\)
• center: \(( 2,0 )\); foci: \(( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )\); vertices: \(( 2,8 ) , ( 2 , - 8 )\)
• B) \(( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1\)
• center: \(( 8,0 )\); foci: \(( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )\); vertices: \(( 8,2 ) , ( 8 , - 2 )\)
• C) \(\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1\)
• center: \(( 2,0 )\); foci: \(( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )\); vertices: \(( 2,8 ) , ( 2 , - 8 )\)
• D) \(\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1\)
• center: \(( 8,0 )\); foci: \(( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )\); vertices: \(( 8,2 )\),
• \(( 8 , - 2 )\)

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Definitions:

Predetermined Overhead Rate

A rate used to apply manufacturing overhead to products or job orders, calculated in advance based on estimated costs.

Variable Manufacturing Overhead

These are manufacturing costs that vary in total directly and proportionately with changes in the production volume, such as indirect materials and utilities.

Direct Labor-Hours

The cumulative working hours of employees directly engaged in manufacturing activities.

Fixed Manufacturing Overhead

Costs in manufacturing that do not change with the level of production, such as salaries of supervisors and rent.