Determine whether the following statements are true and give an explanation or counterexample.

a. A set of parametric equations for a given curve is always unique.

b. The equations x = e^t, y = 2e^t, for -∞ < t < ∞, describe a line passing through the origin with slope 2.

c. The polar coordinates (3, -3π/4) and (-3, 3π/4) describe the same point in the plane.

d. The area of the region between the inner and outer loops of the limaçon

e. The hyperbola y²/2 - x²/4 = 1 has no x-intercept.

f. The equation x² + 4y² - 2x = 3 describes an ellipse.

Transcribed Image Text:

1 f(0)² d0. r = f(0) = 1 – 4 cos 0 is 2. %3D