Answers to Odd Exercises on Ellipses Centered at the Origin

 

1.  For the ellipse

              x2            y2    
                     +                  =  1
             9              4

the x-axis the MAJOR axis and the y-axis is the MINOR axis.

3.  Ellipses are never graphs of functions.

True, since they will never pass the vertical line test.

 

5.          x2            y2    
                     +                  =  1
            25             9

7.          x2            y2    
                     +                  =  1
            36            49

9.                    y2    
           x2  +                 =  1
                        4

11.         x2            y2    
                    +                  =  1
             5             16

13.                      y2    
           9x2  +                 =  1
                         4

15.     25x2  +  y2  =  1

               

17.     4x2  +  9y2  =  1

19.     3x2  +  10y2  =  1

21.     x2  +  4y2  =  16

23.     x2  +  25y2  =  25

25.     x2  +  4y2  =  9

27.     25x2  +  36y2  =  9

29.     9x2  +  12y2  =  12

31.     x2  +  10y2  =  5

33.          

            x2             y2    
                     +                  =  1
            9             16

 

35. 

             x2            y2    
                     +                =  1
            16            4

 

 

37. 

                     y2    
        x2  +              =  1
                     4

39.  Two of the vertices of an ellipse centered at the origin are (3,0) and (0,-4).  What are the other two vertices?

        (-3,0) and (0,4)

41.  One of the vertices of an ellipse centered at the origin is (3,0).  If the ellipse passes through the point (1,8/3), find the equation of the ellipse.

            x2             y2    
                     +                  =  1
            4             100

43.  One of the vertices of an ellipse centered at the origin is (-3,0).  If the ellipse passes through the point (,2), find the equation of the ellipse.

            x2             y2    
                     +                  =  1
            9              36

 


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