Find the Standard Form of the Equation of the Hyperbola $y = \frac { 5 } { 2 } x , y = - \frac { 5 } { 2 } x$

question 148

Multiple Choice

Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: (1, -2) , (5, -2)
Asymptotes: $y = \frac { 5 } { 2 } x , y = - \frac { 5 } { 2 } x$

• A) \(\frac { ( y - 3 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 25 } = 1\)
• B) \(\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1\)
• C) \(\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1\)
• D) \(\frac { ( x - 3 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1\)
• E) \(\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1\)

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Definitions:

Abdominal Aorta

The major blood vessel that runs from the heart through the center of the chest and abdomen, supplying oxygenated blood to the abdominal and pelvic organs and the legs.

Thoracic Aorta

The section of the aorta that runs through the thorax, supplying oxygenated blood to the chest and upper abdominal area.

Aortic Arch

The curved portion of the aorta, the major blood vessel, which emerges from the heart and arcs down to the chest and abdomen.

Posterior Tibial Artery

A major artery of the lower leg that supplies blood to the posterior compartment of the leg and the sole of the foot.