Question

The eccentricity of the curve represented by $ x = 3 (\cos t + \sin t) $, $ y = 4 (\cos t - \sin t) $ is:

• A. \( \frac{\sqrt{7}}{4} \)
• B. \( \frac{1}{16} \)
• C. \( \frac{\sqrt{7}}{3} \)
• D. \( \frac{\sqrt{8}}{4} \)

Hint:

For parametric curves, use the chain rule to find \( \frac{dy}{dx} \) and then calculate the eccentricity using the formula \( e = \sqrt{1 + \left( \frac{dy}{dx} \right)^2} \).