Find the Standard-Form Equation of the Hyperbola Centered at the Origin

question 282

Multiple Choice

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Foci at $( - 20,0 ) , ( 20,0 )$ ; asymptotes: $y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$

• A) \(\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 144 } = 1\)
• B) \(\frac { x ^ { 2 } } { 256 } - \frac { y ^ { 2 } } { 144 } = 1\)
• C) \(\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1\)
• D) \(\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 1\)

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Definitions:

Cystic Duct

A short duct that connects the gallbladder to the common bile duct, which then carries bile to the intestine.

Hepatic Duct

The duct that carries bile from the liver into the common bile duct, which then heads towards the gallbladder or intestine.

Pancreatic Duct

A channel in the pancreas that transports digestive enzymes and bicarbonate from the pancreas to the duodenum.

Parotid Salivary Gland

One of the major salivary glands located near the ear, responsible for producing saliva to facilitate chewing and swallowing.