Find the Standard Form of the Equation of the Ellipse $( 5,3 ) , ( 5,13 )$

question 332

Multiple Choice

Find the standard form of the equation of the ellipse with the given characteristics.
Foci: $( 5,3 ) , ( 5,13 )$ , endpoints of the major axis: $( 5,0 ) , ( 5,16 )$

• A) \(\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 39 } = 1\)
• B) \(\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y - 8 ) ^ { 2 } } { 39 } = 1\)
• C) \(\frac { ( x - 5 ) ^ { 2 } } { 39 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1\)
• D) \(\frac { ( x + 5 ) ^ { 2 } } { 39 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1\)
• E) \(\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 39 } = 1\)

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Definitions:

Magnetism

A physical property of materials that respond to the magnetic field, often resulting from the motion of electric charges.

Rock Types

Categories into which rocks are classified based on their formation process, including igneous, sedimentary, and metamorphic rocks.

Pluton

A pluton is a body of intrusive igneous rock that crystallized from magma slowly cooling below the surface of the Earth, often forming the core of mountains.

Sedimentary Unit

A layer of sedimentary rock with distinct physical, chemical, or biological characteristics that distinguish it from adjacent layers.