Find an Equation for the Orthogonal Trajectories of the Given $8 x ^ { 2 } + y = C$

question 13

Multiple Choice

Find an equation for the orthogonal trajectories of the given family of curves. $8 x ^ { 2 } + y = C$

• A) \(y - \ln x ^ { 16 } = C\)
• B) \(y - x e ^ { 1 / 16 } = C\)
• C) \(y - \ln x ^ { 1 / 6 } = C\)
• D) \(\ln y - x ^ { 1 / 6 } = C\)

---

Definitions:

Wage Rate

The standard amount of compensation paid to an employee per unit of time (e.g., hourly, daily, or annually) for their labor.

Consumption

The process by which goods and services are utilized by consumers to satisfy their needs and desires.

Budget Equation

An equation that represents the balance between an individual's or entity's income and expenses.

Leisure

Time spent not working and free from obligations, often dedicated to relaxation or enjoyment.