Convert the Equation to the Standard Form for a Hyperbola $$9 x ^ { 2 } - 4 y ^ { 2 } - 36 x - 8 y - 4 = 0$$

question 50

Multiple Choice

Convert the equation to the standard form for a hyperbola by completing the square.
- $$9 x ^ { 2 } - 4 y ^ { 2 } - 36 x - 8 y - 4 = 0$$

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

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Definitions:

Deadweight Loss

A shortfall in economic optimization that occurs when the balance for a good or service is missed or impossible to hit.

Tax

A compulsory financial charge or levy imposed by a government on individuals or entities to fund public expenditure.

Consumer Surplus

The difference between the aggregate willingness to pay by consumers for a good or service and the aggregate actual payment.

Deadweight Loss

An economic inefficiency caused by a disruption in market equilibrium, leading to a loss of societal welfare.