Solve the Problem $( 0,4 )$ And Then Moves Closer and Closer to the Line

question 74

Multiple Choice

Solve the problem.
-A satellite following the hyperbolic path shown in the picture turns rapidly at $( 0,4 )$ and then moves closer and closer to the line $y = \frac { 8 } { 5 } x$ as it gets farther from the tracking station at the origin. Find the equation that describes the path of the rocket if the center of the hyperbola is at $( 0,0 )$ .

• A) \(\frac { y ^ { 2 } } { \frac { 25 } { 4 } } - \frac { x ^ { 2 } } { 16 } = 1\)
• B) \(\frac { x ^ { 2 } } { \left( \frac { 12 } { 5 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1\)
• C) \(\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { \left( \frac { 16 } { 5 } \right) ^ { 2 } } = 1\)
• D) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { \frac { 25 } { 4 } } = 1\)

---

Definitions:

Unemployment Insurance

A government program that provides financial assistance to eligible workers who are unemployed through no fault of their own, offering temporary income support.

Employee Wages

The compensation paid to employees for their labor, including hourly wages, salaries, and other forms of payment for work performed.

Merit Rating

A system of evaluating employees or operations based on performance, often utilized in determining pay raises or operational improvements.

FICA Taxes

Taxes imposed on both employees and employers to fund Social Security and Medicare, based on a percentage of the employee's earnings.