Complete the Square to Determine the Type of Curve Represented $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

question 53

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

• A) \(\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1\)
• , ellipse
• B) \(9 ( x - 2 ) ^ { 2 } - 4 y ^ { 2 } = 9\)
• , hyperbola
• C) \(\frac { x ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1\)
• , ellipse
• D) \(\frac { ( x - 2 ) ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1\)
• , hyperbola
• E) \(\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1\)
• , ellipse

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Definitions:

Sales Mix

The combination of products or services that a company sells, typically influencing the company's profits and strategy.

High-margin Items

Products or services that generate a significantly higher percentage of profit relative to their sales price.

Incremental Analysis

An analytical approach that focuses only on those costs and revenues that change as a result of a decision.

Break-even Point

The point at which total revenues equal total costs, resulting in no net loss or gain for the business.