# Describe the shape of the graph of the parametric equation: x(t) = a cos(t) y(t) = b sin(t), 0 ≤ t ≤ 2π

MATH 005B Chapter 10 material 40 pts quiz – 5 pts each:

Use notes, book as needed – Due December 12

1. A) Describe the shape of the graph of the parametric equation: x(t) = a cos(t) y(t) = b sin(t), 0 ≤ t ≤ 2π

B) Find an equation for the tangent line to the above equation at t = arctan(4/3)

2. A) Sketch a graph of the rectangular function: y = 3 sin(x) +2

B) Use this to sketch a graph of the polar function: r(θ) = 3 sin(θ) + 2

3. Below is the graph of r(θ) = 3 sin(3 θ):

A) Find an equation for the tangent line at the point shown.

B) Find all places where the graph has vertical tangents

C) Find the area of one loop.

4. Find an equation for the parabola with focus (5, -2) and directrix y = 4.

5. Locate the center, foci, and endpoints of major and minor axes for the ellipse:

6×2 + 5y2 + 12x + 40y – 34 = 0.

6. Find an equation for the ellipse inscribed in the rectangle with

upper left corner: (-3, 7) and lower right corner (7, -1).

7. Locate the center, vertices, foci and equations of asymptotes for the hyperbola:

3×2 – 4y2 + 18x + 16y = 0

8. Find an equation for the hyperbola with asymptotes: y = 2x + 3 and y = -2x + 7 and one focus at (0, 5).