Find the Center, Transverse Axis, Vertices, Foci, and Asymptotes of the Hyperbola

question 54

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$$

• A) center at \(( 4 , - 1 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 0 , - 1 )\) and \(( 8 , - 1 )\)
• foci at \(( 4 - \sqrt { 41 } , - 1 )\) and \(( 4 + \sqrt { 41 } , - 1 )\)
• asymptotes of \(y + 1 = - \frac { 5 } { 4 } ( x - 4 )\) and \(y + 1 = \frac { 5 } { 4 } ( x - 4 )\)
• B) center at \(( - 1,4 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 6,4 )\) and \(( 4,4 )\)
• foci at \(( - 1 - \sqrt { 41 } , 4 )\) and \(( - 1 + \sqrt { 41 } , 4 )\)
• asymptotes of \(y - 4 = - \frac { 4 } { 5 } ( x + 1 )\) and \(y - 4 = \frac { 4 } { 5 } ( x + 1 )\)
• C) center at \(( 4 , - 1 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices at \(( 4 , - 6 )\) and \(( 4,4 )\)
• foci at \(( 4 , - 1 - \sqrt { 41 } )\) and \(( 4 , - 1 + \sqrt { 41 } )\)
• asymptotes of \(y - 1 = - \frac { 5 } { 4 } ( x + 4 )\) and \(y - 1 = \frac { 5 } { 4 } ( x + 4 )\)
• D) center at \(( 4 , - 1 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 1 , - 1 )\) and \(( 9 , - 1 )\)
• foci at \(( 4 - \sqrt { 41 } , - 1 )\) and \(( 4 + \sqrt { 41 } , - 1 )\)
• asymptotes of \(y + 1 = - \frac { 4 } { 5 } ( x - 4 )\) and \(y + 1 = \frac { 4 } { 5 } ( x - 4 )\)

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Marginal Tax Rate

The rate at which the last dollar of income is taxed, indicating the percentage of tax applied to your income for each tax bracket in which you qualify.

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A taxation system where the tax rate remains constant regardless of the amount of income.

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The percentage representation of total taxes paid in relation to the overall taxable income or expenditure.

Marginal Tax Rate

The rate at which the last dollar of income is taxed, influencing decisions about whether to engage in activities that will produce additional income.