Question 870212: The ellipse with one focus at (2,5) and minor vertices at (-1,7) and (-1,3)
Graph the conic and find its equation in standard form
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! The midpoint of the minor vertices will be the center of the ellipse. Knowing this lets you also determine the other focus.
 , so the center of the ellipse is (-1,5).
If one focus is (2,5), then the other focus is on the other side of (-1,5), and is |-1-2|=3 units away. Starting at (-1,5), moving to the left by 3 units puts the focus at (-4,5). No matter. The focal length is c=3.
Looking at minor vertices, distance from 7 to 3 is 4; half of this is  . This means, b=2.
EQUATION: 
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