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

question 66

Multiple Choice

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

• A) center at \(( 1 , - 2 )\)
• foci at \(( 1 + 3 \sqrt { 3 } , 1 ) , ( 1 - 3 \sqrt { 3 } , 1 )\)
• vertices at \(( 6 , - 2 ) , ( - 6 , - 2 )\)
• B) center at \(( - 2,1 )\)
• foci at \(( - 2 + 3 \sqrt { 3 } , 1 ) , ( - 2 - 3 \sqrt { 3 } , 1 )\)
• vertices at \(( - 5 , - 2 ) , ( 7 , - 2 )\)
• C) center at \(( 1 , - 2 )\)
• foci at \(( - 3 \sqrt { 3 } , - 2 ) , ( 3 \sqrt { 3 } , - 2 )\)
• vertices at \(( 6 , - 2 ) , ( - 6 , - 2 )\)
• D) center at \(( 1 , - 2 )\)
• foci at \(( 1 + 3 \sqrt { 3 } , - 2 ) , ( 1 - 3 \sqrt { 3 } , - 2 )\)
• vertices at \(( - 5 , - 2 ) , ( 7 , - 2 )\)

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Definitions:

Contralateral Neglect

A neurological condition often resulting from damage to the brain's right hemisphere, causing the affected individual to ignore or neglect the left side of their body or the environment.

Planning

The process of making detailed strategies or arrangements beforehand for achieving future goals.

Brain Areas

Distinct regions within the brain specialized for various cognitive, sensory, or motor functions.

Cerebral Asymmetry

The functional and structural differences between the brain's left and right hemispheres, often associated with specific cognitive processes and abilities.