Chapter 9 Review (1).docx

PreCalculus Ch. 9 Review

Name:

Determine the vertex, focus and directrix of each parabola and sketch its graph. 1.

(𝑥 − 2)2 = 4(𝑦 + 1)

Vertex: Focus: Directrix: Graph:

Determine the standard form equation for a parabola with the following characteristics. 2.

Vertex (−3, −5); directrix 𝑦 = 5

Determine the center, vertices, foci, and eccentricity of each ellipse and sketch each graph. 3.

𝑥2 64

+

𝑦2 121

=1

4.

−36𝑥 2 + 16𝑦 2 − 288𝑥 + 64𝑦 + 64 = 0

Center:

Center:

Foci:

Foci:

Vertices:

Vertices:

Graph:

Graph:

Write the standard form equation of an ellipse with the following characteristics. 5.

Foci (1,7) and (1, −3); major axis of length 12

Determine the center, vertices, foci, and asymptotes of each hyperbola and sketch each graph. 6.

(𝑦+2)2 4

−

(𝑥+1)2 81

7.

=1

Center:

Center:

Foci:

Foci:

Graph:

Graph:

4𝑥 2 − 24𝑥 − 9𝑦 2 − 90𝑦 − 153 = 0

Determine the standard form equation of the hyperbola with the following characteristics. 8.

Foci (0,2) and (10,2); transverse axis of length 8

Without graphing, determine the type of conic each equation is. 9.

3𝑥 2 − 2𝑦 2 + 4𝑦 − 3 = 0

10. 2𝑦 2 − 3𝑥 + 2 = 0 11. 8𝑥 2 + 8𝑦 2 − 17𝑥 = 98 12. 4x 2 + 4y 2 − 2x − 3 =0

13. For the parametric equations: 𝑥 = √𝑡 and 𝑦 = 𝑡 + 1 a. Complete the table t

x

y

0

b.

Plot the points from part a to sketch a graph of the parametric equations. Remember to use arrows to indicate the direction of the curve.

1 4 9 c.

Find the rectangular equation by eliminating the parameter.

d.

Describe any differences between the parametric equations and the rectangular equation you found.

14. Eliminate the parameter t to obtain the rectangular equation. Then sketch a graph of the equation, using arrows to show the direction of the curve. 𝑥 = 4𝑐𝑜𝑠𝑡, 𝑦 = 4𝑠𝑖𝑛𝑡; 0 ≤ 𝑡 ≤ 2𝜋

15. Plot the following points on the polar coordinate graph: 2𝜋

e.

(4,

f.

(−3,

g.

(5, − )

h.

(−2, −

3

)

3𝜋 4

)

𝜋 6

4𝜋 3

)

16. Determine 3 additional sets of polar coordinates for the point

17. Find the rectangular coordinates

𝜋

of the point (−3,

(3, − ) in the range [−2𝜋, 2𝜋]

5𝜋 4

18. Find the polar coordinates of the point (4, −4).

).

3

19. Convert the equations into rectangular form. i. 𝑟 = −3𝑐𝑜𝑠𝜃

j.

𝑟 = 2𝑐𝑠𝑐𝜃

20. Convert the equations into polar form. k. 𝑦 = 2𝑥 + 3

l.

𝑥+𝑦=2

21. Covert the following polar equations to rectangular and graph (no calculator) m. 𝜃 =

n.

5𝜋

o.

6

𝑟𝑐𝑜𝑠 𝜃 = −2

p.

𝑟𝑠𝑖𝑛𝜃 = 3

𝑟 = −4