Write the Equation of the Ellipse in Standard Form $$36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$$

question 90

Multiple Choice

Write the equation of the ellipse in standard form. Identify the vertices and foci.
- $$36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$$

• A) \(\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1\)
• vertices: \(\left( - \frac { 9 } { 5 } , 0 \right) , \left( - \frac { 11 } { 5 } , 0 \right)\)
• foci: \(\left( 2 + \frac { \sqrt { 11 } } { 30 } , 0 \right) , \left( 2 - \frac { \sqrt { 11 } } { 30 } , 0 \right)\)
• B) \(\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1\)
• vertices: \(\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)\)
• foci: \(\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)\)
• C) \(36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1\)
• vertices: \(( 36 , - 2 ) , ( - 36 , - 2 )\)
• foci: \(\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)\)
• D) \(36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1\)
• vertices: \(\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)\)
• foci: \(\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)\)

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Definitions:

Capitalism

An economic system characterized by private ownership of the means of production and the creation of goods or services for profit.

Inequality

The state of being unequal, particularly in terms of income, wealth, opportunities, and status among individuals or groups.

Hegemonic Masculinity

A concept describing the norms that dictate the dominant form of masculinity within a particular culture, often marginalized other masculinities and femininities.

Bourgeois

A term that describes the middle class, particularly those with capitalist interests and values, often contrasted with the proletariat in Marxist contexts.