SOLUTION: Find the equation of the ellipse with a vertex at (4,10), and foci at (4,2) and (4,8)

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Question 955294: Find the equation of the ellipse with a vertex at (4,10), and foci at (4,2) and (4,8)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The foci allow finding the center, and then that one given vertex lets you know value for variable a.

CENTER: On line x=4, y value is %282%2B8%29%2F2=5.

Note that foci are in a vertical arrangement so "a" goes under the y-rational expression. a=10-5=5.

Currently we have a=5 and highlight_green%28%28x-4%29%5E2%2Fb%5E2%2B%28y-5%29%5E2%2F%285%5E2%29=1%29.

a%5E2=b%5E2%2Bc%5E2, from the graph and derivation of an ellipse with vertical axis of symmetry or either horizontal axis of symmetry.
How far is center from either focus? 3=c.
What was a? a=5.
Find b.
b%5E2=a%5E2-c%5E2
b%5E2=25-9
b%5E2=16
b=4

Finish the equation:
highlight%28%28x-4%29%5E2%2F4%5E2%2B%28y-5%29%5E2%2F%285%5E2%29=1%29