Calculus-Sec-10-5-Solution

10.5        Conic Sections                  by SGLee - HSKim - SWSun

1-4. Sketch the parabola with the given equation. Show and label its vertex, focus, axis, and directrix.

1.

vertex :  / focus :  / axis :  / directrix : .

2.

vertex :  / focus :  / axis :  / directrix : .

3.

vertex :  / focus :  / axis :  / directrix : .

4.

6.

7.

8.

9-11. Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph.

9.

11.

12-14. Identify the type of conic section whose equation is given and find the vertices and foci.

12.

⇒   ⇒   ⇒ : Ellipse.

13.

⇒  : Parabola with vertices (1,2) and focus (3,2).

14.

⇒  : Hyperbola with vertices  and focus (-2,4), (-2,-2)

15-22. Find an equation for the conic that satisfies the given conditions.

15. Parabola, vertex , focus

16. Parabola, vertex , focus

.

17. Ellipse, foci , vertices

.

18. Ellipse, foci , vertices

.

19. Ellipse, center , focus  vertex

.

21. Hyperbola, foci , asymptotes

.

20. Hyperbola, foci , vertices

.

22. Hyperbola, focus , asymptotes  and

.

23-28. Write a polar equation of a conic with the focus at the origin and the given data.

23. Hyperbola, eccentricity , directrix

.

24. Hyperbola, eccentricity , directrix

.

25. Ellipse, eccentricity , directrix

.

26. Ellipse, eccentricity , directrix

.

27. Parabola, eccentricity , directrix

.

28. Parabola, eccentricity , directrix

.

29-32. Find the eccentricity, identify the conic, give an equation of the directrix, and sketch the conic.

29.

, Parabola , directrix : .

30.

, Parabola , directrix : .

31.

, Ellipse, directrix : .

32.

, Ellipse, directrix : .