Find the Center, Foci, and Vertices of the Ellipse $$\frac { ( x - 2 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$$

question 21

Multiple Choice

Find the center, foci, and vertices of the ellipse.
- $$\frac { ( x - 2 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$$

• A) center at \(( - 3,2 )\)
• foci at \(( - 3 + 3 \sqrt { 3 } , 2 ) , ( - 3 - 3 \sqrt { 3 } , 2 )\)
• vertices at \(( - 4 , - 3 ) , ( 8 , - 3 )\)
• B) center at \(( 2 , - 3 )\)
• foci at \(( 2 + 3 \sqrt { 3 } , 2 ) , ( 2 - 3 \sqrt { 3 } , 2 )\)
• vertices at \(( 6 , - 3 ) , ( - 6 , - 3 )\)
• C) center at \(( 2 , - 3 )\)
• foci at \(( - 3 \sqrt { 3 } , - 3 ) , ( 3 \sqrt { 3 } , - 3 )\)
• vertices at \(( 6 , - 3 ) , ( - 6 , - 3 )\)
• D) center at \(( 2 , - 3 )\)
• foci at \(( 2 + 3 \sqrt { 3 } , - 3 ) , ( 2 - 3 \sqrt { 3 } , - 3 )\)
• vertices at \(( - 4 , - 3 ) , ( 8 , - 3 )\)

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Definitions:

Duopoly

Duopoly is a market structure characterized by two firms controlling the majority of the market share, often leading to strategic behavior in price and output decisions.

Profit

The financial gain achieved when the amount of revenue gained from a business activity exceeds the expenses, costs, and taxes needed to sustain the activity.

Collusion

An agreement among firms, usually in secret, to fix prices or to divide markets among themselves, which restricts competition.

Fix Prices

Fix prices involves setting product or service prices at a certain level, often agreed upon among competitors to avoid undercutting each other, which is illegal in many jurisdictions.