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Question 750433: i dont understand how to graph the vertical ellipse whose center is at (3,2), minor axis is 6, and has a vertex at (3,-3). please help
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You are given the coordinates of the center and one vertex, so you can plot those point right away.
You are also given the horizontal width of ellipse, the 6 units that are the length of the minor axis.
I indicated the above information in red on the diagram below:
 The vertex given is 5 units below the center, so the other vertex must be 5 units above the center, at (3,7).
Since the whole minor axis is 6 units long, each end will be 3 units from the center. That puts the ends of the minor axis at (0,2) and (6,2). Those two points are called the co-vertices.
The second vertex and the co-vertices are marked in blue in the diagram.
The next and final step is sketching a curve that looks like an ellipse and goes through the vertices and co-vertices. The ellipse is drawn in green in the diagram.
If you sketch your ellipse by hand, going through the vertices and co-vertices it should be acceptable, even though the other points will not be accurately placed.
NOTE:
If it was required, you would have to locate the foci.
The distances from the center to the vertices, co-vertices, and foci are represented by a, b, and c.
 = distance to vertex (semi-major axis)
 = distance to co-vertex (semi-minor axis)
 = distance to focus (focal distance)
They are related by 
In your case,  -->  -->  --> 
So the foci wouldbe 4 units above and below the center, at (3,6) and (3,-2).
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