Graph Hyperbolas Not Centered at the Origin
- $$( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$$

question 187

Multiple Choice

Graph Hyperbolas Not Centered at the Origin
- $$( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$$

• A) Center: \(( - 2,3 )\); Vertices: \(( - 10,3 )\) and \(( 6,3 )\); Foci: \(( - 2 - \sqrt { 65 } , 3 )\) and \(( - 2 + \sqrt { 65 } , 3 )\)
• B) Center: \(( 2 , - 3 )\); Vertices: \(( - 6 , - 3 )\) and \(( 10 , - 3 )\); Foci: \(( 2 - \sqrt { 65 } , 3 )\) and \(( 2 + \sqrt { 65 } , 3 )\)
• C) Center: \(( - 2,3 )\); Vertices: \(( - 9,4 )\) and \(( 7,4 )\); Foci: \(( - 1 - \sqrt { 65 } , 4 )\) and \(( - 1 + \sqrt { 65 } , 4 )\)
• D) Center: \(( - 2,3 )\); Vertices: \(( 8,3 )\) and \(( - 8,3 )\); Foci: \(( - \sqrt { 65 } , 3 )\) and \(( \sqrt { 65 } , 3 )\)

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Definitions:

MC Curve

Marginal Cost Curve, which depicts the change in total cost that arises when the quantity produced is incremented by one unit.

AVC Curve

Stands for Average Variable Cost Curve, a graphical representation that shows the average variable costs of production at different levels of output.

ATC Curves

The graphical representation of the relationship between average total costs and output levels in the short run for a firm.

Diseconomies of Scale

Diseconomies of scale occur when a business expands to the point where the costs of managing and coordinating operations increase, leading to a rise in the average costs.