PC

Spring Semester Exam Review

ASN

Unit 7—Parametric and Polar Equations

Simplify the following algebraic expressions using the properties of exponents. 0 5𝑎𝑎 2 𝑏𝑏𝑐𝑐 5 3𝑎𝑎𝑏𝑏−2 4𝑏𝑏2 𝑐𝑐 3 � � � � 9 � 2𝑎𝑎 3 𝑏𝑏3 𝑐𝑐 𝑎𝑎𝑏𝑏2 𝑐𝑐 𝑎𝑎𝑐𝑐

1. (3𝑥𝑥 2 𝑦𝑦)3 ∙ (2𝑥𝑥𝑦𝑦 4 )

2. �

Graph the following parametric equations. Be sure to plot your points correctly. 3. 𝑥𝑥 = 2𝑡𝑡 2 − 1 4. 𝑥𝑥 = 5 sin 𝑡𝑡 𝑦𝑦 = 𝑡𝑡 𝑦𝑦 = 5 cos 𝑡𝑡 0≤𝑡𝑡≤3 0≤𝑡𝑡≤𝜋𝜋

Find the parameterization for the curve. Eliminate the parameter and identify the graph of the parametric curve. 5. The line segment with endpoints (5,7) and (3, −1). 6. The circle with center at (−5, −4) and radius of √17. Convert the polar coordinates to rectangular coordinates 7. �7,

5𝜋𝜋 � 6

8. (3,4.1)

Convert the rectangular coordinates to polar coordinates with the given limitations. 9. (−2, −7), 0 ≤ 𝜃𝜃 ≤ 2𝜋𝜋 10.(5, −1), 0 ≤ 𝜃𝜃 ≤ 2𝜋𝜋 Convert the polar equation to rectangular form. 11.𝑟𝑟 csc 𝜃𝜃 = 2 12.𝑟𝑟 = 4 cos 𝜃𝜃 − 4 sin 𝜃𝜃 Convert the rectangular equation to polar form. 13.3𝑥𝑥 + 4𝑦𝑦 = 4 14.𝑥𝑥 2 + (𝑦𝑦 − 3)2 = 9

Determine the minimum interval for the graph of the polar curve. 15.𝑟𝑟 = 6 − 5 cos 𝜃𝜃 16.𝑟𝑟 = 𝜃𝜃⁄4

Unit 8—Conic Sections Graph the given information, write the equation of the conic section in standard form.

17.A parabola with vertex at (2, 3) and a focus at (2, 2). 18.An ellipse with foci at (1, 0) and (−1, 0) and minor axis of length of 4.

Graph the conic section, label all the important features.

19.

(𝑦𝑦+6)2 64

−

(𝑥𝑥−3)2 35

=1

21.(𝑥𝑥 − 5)2 = 12(𝑦𝑦 + 4)

20.

(𝑥𝑥+2)2 16

+

(𝑦𝑦−1)2 36

=1

22.(𝑥𝑥 − 2)2 + 𝑦𝑦 2 = 100

Identify the conic, put it in standard form, and identify the important characteristics.

23.4𝑥𝑥 2 + 9𝑦𝑦 2 = 36 25.2𝑥𝑥 2 − 4𝑥𝑥 − 𝑦𝑦 − 2 = −3

24.2𝑥𝑥 2 + 2𝑦𝑦 2 + 20𝑥𝑥 − 8𝑦𝑦 + 38 = −2 26.𝑥𝑥 2 − 3𝑦𝑦 2 + 6𝑦𝑦 − 4 = 1

Write the equation in standard form given the following information.

27.A hyperbola with a center at (−1, 2), vertex at (−4, 2) and a focus at (−6, 2). 28.A parabola with vertex at (−1, 4), focus at (−1, 6).