Find the Standard-Form Equation for an Ellipse Which Satisfies the Given

question 222

Multiple Choice

Find the standard-form equation for an ellipse which satisfies the given conditions.
-An ellipse centered at the origin having focus at $( 8,0 )$ and eccentricity equal to $\frac { 1 } { 2 }$

• A) \(\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 48 } = 1\)
• B) \(\frac { y ^ { 2 } } { 256 } + \frac { x ^ { 2 } } { 192 } = 1\)
• C) \(\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 192 } = 1\)
• D) \(\frac { x ^ { 2 } } { 64 } + y ^ { 2 } = 1\)

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Definitions:

Ediacaran Fauna

Ediacaran fauna is a group of animal species that existed during the Ediacaran period, just before the Cambrian. The oldest Ediacaran fossils are about 570 million years old. Ediacarans included diverse species that looked like fronds, geometrical disks, and blobs covered with tire tracks. They appear to have become extinct 540 million years ago, although some researchers argue that certain Ediacaran taxa belong to extant animal clades.

Extinction

Refers to the permanent loss of a species. It is marked by the death or failure to breed of the last individual.

Stromatolites

Layered structures formed by the mineralization of bacteria.

Zircons

Minerals that are widely used in dating geological structures due to their ability to encapsulate and preserve uranium-lead isotopes over immense periods.