Calculus-Sec-10-5-Solution


  10.5        Conic Sections                  by SGLee - HSKim - SWSun

                                                                                                             http://youtu.be/LRmasW9uqYY

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

 

 1. 

           http://matrix.skku.ac.kr/cal-lab/cal-9-5-1.html 

 

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




 2. 

           http://matrix.skku.ac.kr/cal-lab/cal-9-5-2.html 

 

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




 3. 

           http://matrix.skku.ac.kr/cal-lab/cal-9-5-3.html 

 

 

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




4. 




 5. 

           http://matrix.skku.ac.kr/cal-lab/cal-9-5-5.html 

 

 
















6. 
















7. 
















8. 
















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

 

 9.  

           http://matrix.skku.ac.kr/cal-lab/cal-9-5-9.html 

 
















 10. 

             http://matrix.skku.ac.kr/cal-lab/cal-9-5-10.html 

 

 
















11. 




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

 

 12. 

            http://matrix.skku.ac.kr/cal-lab/cal-9-5-12.html 

 

 

       ⇒   ⇒   ⇒ : Ellipse.  
















 13. 

            http://matrix.skku.ac.kr/cal-lab/cal-9-5-13.html 

 

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




 14. 

            http://matrix.skku.ac.kr/cal-lab/cal-9-5-14.html 

 

 

      ⇒  : 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 

     http://math1.skku.ac.kr/home/mm2013/631/

 

 

     

               Answer:   .




16. Parabola, vertex , focus 

 

     .




17. Ellipse, foci , vertices 

     http://math1.skku.ac.kr/home/mm2013/632/

 

  .




18. Ellipse, foci , vertices 

 

 

    .




19. Ellipse, center , focus  vertex 

 

     .




21. Hyperbola, foci , asymptotes 

 

     .




20. Hyperbola, foci , vertices 

     http://math1.skku.ac.kr/home/mm2013/633/

 

 .




 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 

     http://math1.skku.ac.kr/home/mm2013/634/

 

     .







24. Hyperbola, eccentricity , directrix 

     http://math1.skku.ac.kr/home/mm2013/635/

 

      .







25. Ellipse, eccentricity , directrix 

     http://math1.skku.ac.kr/home/mm2013/637/

 

      .







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 : .




                                                   

 

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