sketch the following in the same coordinate system and clearly label the axes:
x^2+(y^2)/4=1, x^2+(y^2)/4+(1/9)=1, x^2+(y^2)/4+(4/9)=1
Unfortunately, as an AI language model, I do not have the capability to create visual images or graphs. However, I can describe how these equations would look when graphed:
- The first equation, x^2+(y^2)/4=1, represents an ellipse centered at the origin with a horizontal major axis of length 2 and a vertical minor axis of length 2√3.
- The second equation, x^2+(y^2)/4+(1/9)=1, represents another ellipse centered at the origin, but with a smaller major axis and a larger minor axis than the first ellipse. Its major axis is horizontal and has a length of 2√2, while its minor axis is vertical and has a length of 6√2.
- The third equation, x^2+(y^2)/4+(4/9)=1, again represents an ellipse centered at the origin, but with an even smaller major axis and an even larger minor axis than the previous two ellipses. Its major axis is horizontal and has a length of 2√5, while its minor axis is vertical and has a length of 6√5.
The x-axis is the horizontal axis running through the center of each ellipse (the origin), while the y-axis is the vertical axis running through the center of each ellipse.