HLRGAATPreISM_35799X_06_ch6

HLRGAATPreISM_35799X_06_ch6 - Chapter 6: Analytic Geometry...

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Chapter 6: Analytic Geometry 6.1: Circles and P ar abolas 1. The equation is that of a circle with center (3, 3) and radius 0. That is, the graph is the point (3, 3). 2. The equation is that of a circle with center (3, 3) and radius . No such graph exists. 3. E. Since is equivalent to , this is a parabola that opens to the right . 4. C. Since is equivalent to , this is a parabola that opens upward . 5. H. Since is equivalent to , this is a parabola that opens downward . 6. B. Since is equivalent to , this is a parabola that opens to the left . 7. F. This is the equation of a circle centered at the origin with radius . 8. A. This is the equation of a circle centered at the point with radius . 9. D. This is the equation of a circle centered at the point with radius . 10. G. This is the equation of a circle centered at the origin with radius . No such graph exists. 11. Here . The equation is . 12. Here . The equation is . 13. A circle that is centered at the origin with has equation . 14. A circle that is centered at the origin with has equation . 15. Here . The equation is . 16. Here . The equation is . 17. The radius is the distance between : Here . The equation is . 18. The radius is the distance between : Here . The equation is . 19. If the center is , the circle must touch the x -axis at the point . The radius is 2. Here . The equation is . 20. If the center is , the circle must touch the y -axis at the point . The radius is 5. Here . The equation is . 21. The center is the midpoint on the diameter between : 22. The radius is the distance from the center to an endpoint : 23. Here . The equation is . 1 x 2 2 2 2 1 1 y 1 3 2 2 5 45 h 5 2, k 5] 3 and r 2 5 1 1 45 2 2 5 45 r 5 2 1 2 2 1 ] 1 22 2 1 1 ] 3 2 3 2 2 5 1 9 1 36 5 1 45 5 3 1 5 1 ] 1, 3 2 1 2, ] 3 2 M 5 a ] 1 1 5 2 , 3 1 1 ] 9 2 2 b 5 1 2, ] 3 2 1 ] 1, 3 2 and 1 5, ] 9 2 1 x 2 5 2 2 1 1 y 1 1 2 2 5 25 h 5 5, k 1 and r 2 5 5 2 5 25 1 0, ] 1 2 1 5, ] 1 2 1 x 1 3 2 2 1 1 y 1 2 2 2 5 4 h 3, k 2 and r 2 5 2 2 5 4 1 ] 3, 0 2 1 ] 3, ] 2 2 1 x 2 2 2 2 1 1 y 1 7 2 2 5 25 h 5 2, k 7 and r 2 5 5 2 5 25 r 5 2 1 2 2 1 ] 2 2 1 1 ] 7 2 1 ] 4 2 5 1 16 1 9 5 5 1 2, ] 7 2 and 1 ] 2, ] 4 2 1 x 1 1 2 2 1 1 y 2 2 2 2 5 25 h 1, k 5 2 and r 2 5 5 2 5 25 r 5 2 1 2 2 1 ] 1 2 1 1 6 2 2 2 2 5 1 9 1 16 5 5 1 ] 1, 2 2 and 1 2, 6 2 a x 1 1 2 b 2 1 a y 1 1 4 b 2 5 144 25 h 1 2 , k 1 4 and r 2 5 a 12 5 b 2 5 144 25 a x 2 2 3 b 2 1 a y 1 4 5 b 2 5 9 49 h 5 2 3 , k 4 5 and r 2 5 a 3 7 b 2 5 9 49 x 2 1 y 2 5 25 r 2 5 5 2 5 25 x 2 1 y 2 5 1 r 2 5 1 2 5 1 1 x 1 2 2 2 1 1 y 2 5 2 2 5 16 h 2, k 5 5 and r 2 5 4 2 5 16 1 x 2 1 2 2 1 1 y 2 4 2 2 5 9 h 5 1, k 5 4 and r 2 5 3 2 5 9 1 ] 4 1 25 5 5 1 ] 3, 4 2 1 25 5 5 1 3, ] 4 2 1 5 1 c 6 0 2 y 2 5 4 a ] 3 4 b x y 2 3 x 1 c 6 0 2 x 2 5 4 a ] 3 4 b y x 2 3 y 1 c 7 0 2 x 2 5 4 a 1 8 b y y 5 2 x 2 1 c 7 0 2 y 2 5 4 a 1 8 b x x 5 2 y 2 1 ] 1
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24. The center is the midpoint on the diameter between : . The radius is the distance from the center to an endpoint : . Here . The equation is .
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This note was uploaded on 09/24/2011 for the course MATH 1310 taught by Professor Marks during the Spring '08 term at University of Houston.

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HLRGAATPreISM_35799X_06_ch6 - Chapter 6: Analytic Geometry...

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