Elimate the parameter and graph the parametric equations …
Besides the below problems you can also use problems at the end of your chapter in your book as well as the class grade and your notes to help you review for the test.
1) Eliminate the parameter and graph the parametric equations below.
a) x = t2
y = t + 4
b) x = 3 + 3cosθ
y = 2 + 5sinθ
2) Plot the polar coordinate (1, π/4) and give three additional polar representations of the point using -2π < θ < 2π
3) Find the rectangular form of (-4, 2π/3).
4) Find the polar form of ( -3, -√3)
5) Convert each into polar form.
a. x2 + y2 – 6y = 0
b. xy = -2
6) Convert each into rectangular form.
a. r = 5
b. r = 8sinθ
c. r2 = cos2θ
7) Sketch each of the below graphs
a. r = 5cosθ
b. r = 3 – 5sinθ
c. r2 = 5sin2θ
d. r = -3cos2θ
e. r = cos5θ
8) Find a polar equation of each conic section with its focus at the pole and the given vertex/vertices and graph each.
a. Parabola with vertex (2, π/2)
b. Ellipse with vertices (5, 0), (1, π)
c. Hyperbola with vertices (1, 0), (7, 0)
Answers:
1) a) y = +/-√x + 4 b) [pic] (Check graphs on calculator)
2) (1, -7π/4), (-1, 5π/4), (-1, -3π/4) 3) (2, -2√3) 4) (2√3, 7π/6)
5) a) r = 6sinθ b) r2 = -2secθcscθ
6) a) x2 + y2 = 25 b) x2 + y2 – 8y = 0 c) (x2 + y2)2 – x2 + y2 = 0
7) Use your calculator to check your answers.
8) a) [pic] b) [pic] c) [pic] (Check graphs on calculator)
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