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Chapter Test Form A Page 1 of 3Chapter 6: College Tr igonometry;
Chapter 8: Coll ege Al gebra and Tr igonometry
Copyright Houghton Mifflin Company. All rights reserved. 245
Topics in Analytic Geometry
NAME ___________________________________________________ DATE
_____________ SCORE ________
In Exercises 1-3, find the vertices and the foci of the conic.
If the conic is a hyperbola, find its asymptotes.
1. 21
8x y= 2.
2 2
19 25
x y+ =
3. 2 24 24 2 31 0x y x y + + = 4. Find the equation in standard
form of an ellipse withcenter ( )3,8 , foci ( )3 11,8+ , ( )3 11,8
, andminor axis of length 10.
5. Find the equation in standard form of the parabola
with directrix 5x= and focus ( )11, 7 .6. Determine the smallest
positive angle of rotation
that can be used to eliminate the xy term of
2 24 2 3 2 10 3 10 5 0x xy y x y+ + + + =
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Page 2 of 3 Chapter Test Form AChapter 6: College Tr igonometry;
Chapter 8: College Al gebra and Tr igonometry
Copyright Houghton Mifflin Company. All rights reserved.246
7. Graph: 3 3sinr = + 8. Graph:6
2 cosr
=
9. Find the rectangular coordinates of the point whose
polar coordinates are ( )3,5 / 6 .10. Write 5x= as an equation
in polar coordinates.
11. Eliminate the parameter of the curve given by
25, 3x t y t= + = +
12. a) Eliminate the parameter of the curve given by
3sin , 4cosx t y t= =
b) Graph the curve given by these parametricequations.
642
60=
45=
30=
642
60=
45=
30=
y
2
4
6
-2
-4
-6
2 4 6-6 -4 -2 x
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Chapter Test Form A Page 3 of 3Chapter 6: College Tr igonometry;
Chapter 8: Coll ege Al gebra and Tr igonometry
Copyright Houghton Mifflin Company. All rights reserved. 247
13. Determine the number of petals generated by
2cos6r =
as varies from 0 to 2 .
14. Write a sentence that explains how the graphs of
1
4
2 sin4
r
=
+ +
and2
4
2 sinr
=
+are related.
15. Find a polar equation of the parabola with focus at
the pole and vertex at ( )1, .16. Find a polar equation of the
ellipse with a focus at
the pole, a vertex at ( )6,0 , and eccentricity 1 / 4 .
17. Find the rectangular form of6
1 sinr
=
. 18. Write a sentence or two that explains the difference
(if any) between the graphs of1
C and2
C , given
2 2
1
2
: 3 , 1 2
: 3 , 1 2
C x t y t
C x t y t
= + = = + =
where tis a real number.
