Determine the Two Equations Necessary to Graph the Hyperbola with a Graphing

question 103

Multiple Choice

Determine the two equations necessary to graph the hyperbola with a graphing calculator.
- $$y ^ { 2 } - 64 x ^ { 2 } = 64$$

• A) \(y = 8 + \sqrt { x ^ { 2 } }\) and \(y = 8 - \sqrt { x ^ { 2 } }\)
• B) \(y = 8 + \sqrt { x ^ { 2 } }\) and \(- y = - 8 - \sqrt { x ^ { 2 } }\)
• C) \(y = 8 x ^ { 2 } + 8\) and \(y = - 8 x ^ { 2 } - 8\)
• D) \(y = 8 \sqrt { x ^ { 2 } + 1 }\) and \(y = - 8 \sqrt { x ^ { 2 } + 1 }\)

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Definitions:

Island Arc

An island arc is a type of archipelago, composed predominantly of a series of volcanoes, which arcs roughly parallel to the boundary of oceanic tectonic plates that are being subducted beneath lighter continental plates.

Continental Rifting

The process by which a continent stretches and splits along a rift zone, potentially leading to the formation of a new ocean basin.

Passive Margin

A continental margin that is not associated with plate boundaries and hence experiences little seismic activity.

Subduction

The process by which one tectonic plate moves under another plate and dives into the mantle, often causing volcanic activity.