Find the Center, Vertices, and Foci of the Ellipse Below $$x ^ { 2 } + 8 y ^ { 2 } = 80$$

question 25

Multiple Choice

Find the center, vertices, and foci of the ellipse below.
$$x ^ { 2 } + 8 y ^ { 2 } = 80$$

• A) Center: \(( 0,0 )\)
• Vertices: \(( 4 \sqrt { 5 } , 0 ) , ( - 4 \sqrt { 5 } , 0 )\)
• Foci: \(( \sqrt { 70 } , 0 ) , ( - \sqrt { 70 } , 0 )\)
• B) Center: \(( 0,0 )\)
• Vertices: \(( 0,10 ) , ( 0 , - 10 )\)
• Foci: \(( 0,24 \sqrt { 11 } ) , ( 0 , - 24 \sqrt { 11 } )\)
• C) Center: \(( 80,10 )\)
• Vertices: \(( 160,10 ) , ( - 160,10 )\)
• Foci: \(( 80 + 24 \sqrt { 11 } , 10 ) , ( 80 - 24 \sqrt { 11 } , 10 )\)
• D) Center: \(( 80,10 )\)
• Vertices: \(( 80,20 ) , ( 80 , - 20 )\)
• Foci: \(( 80,10 + 24 \sqrt { 11 } ) , ( 80,10 - 24 \sqrt { 11 } )\)
• E) Center: \(( 0,0 )\)
• Vertices: \(( 80,0 ) , ( - 80,0 )\)
• Foci: \(( 6336,0 ) , ( - 6336,0 )\)

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Definitions:

Spectral Data

Information derived from spectrometry, which provides insights into the structure and composition of substances by analyzing their electromagnetic spectrum.

NMR

Nuclear Magnetic Resonance, a spectroscopic technique used to obtain structural information about molecules based on the interaction of nuclear spins when placed in a magnetic field.

IR

Infrared spectroscopy, a technique used to analyze and identify chemical substances based on their interaction with infrared light.

MS

Mass spectrometry, an analytical technique used to measure the mass-to-charge ratio of ions, useful in determining the composition of a sample or molecule.