Solve Applied Problems Involving Hyperbolas
-A Satellite Following the Hyperbolic $( 0,6 )$

question 83

Multiple Choice

Solve Applied Problems Involving Hyperbolas
-A satellite following the hyperbolic path shown in the picture turns rapidly at $( 0,6 )$ and then moves closer and closer to the line $y = \frac { 9 } { 2 } x$ as it gets farther from the tracking station at the origin. Find the equation that describes the path of the satellite if the center of the hyperbola is at $( 0,0 )$ .

• A) \(\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { \frac { 16 } { 9 } } = 1\)
• B) \(\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { \left( \frac { 54 } { 4 } \right) ^ { 2 } } = 1\)
• C) \(\frac { y ^ { 2 } } { \frac { 16 } { 9 } } - \frac { x ^ { 2 } } { 36 } = 1\)
• D) \(\frac { x ^ { 2 } } { \left( \frac { 54 } { 4 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 36 } = 1\)

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Definitions:

Reshoring

The process of bringing back manufacturing and services to a country from overseas to strengthen the local economy and reduce reliance on foreign suppliers.

Minimum Efficient Scale

The smallest production quantity at which the long-run, total average cost is minimized.

Economies of Scale

Refers to the cost advantage that arises with increased output of a product, leading to a reduction in the per-unit cost.

Production Process

A sequence of steps or operations involved in the manufacture of goods or the delivery of services.