SOLUTION: Find an equation of the ellipse that satisfies the given conditions: Center (3,0), one focus at (3,2), length of minor axis is 4

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Question 1177460: Find an equation of the ellipse that satisfies the given conditions:
Center (3,0), one focus at (3,2), length of minor axis is 4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
Center (3,0)
one focus at (3,2)
length of minor axis is 4

Equation of the ellipse:
since center and foci have same x coordinate, major axis is vertical, so you need equation
%28x-h%29%5E2%2Fb%5E2+%2B%28y-k%29%5E2%2Fa%5E2+=1
Center (3,0) =>+h=3, k=0
focus at (3,2)-> c=2
minor axis is 2b=4 ->b=2
Use the equation c%5E2=a%5E2-b%5E2 along with the given coordinates of the vertices and foci, to solve for b%5E2.
a%5E2=c%5E2%2Bb%5E2
a%5E2=2%5E2%2B2%5E2
a%5E2=8
a=sqrt%288%29
a=sqrt%284%2A2%29
a=2sqrt%282%29

%28x-3%29%5E2%2F4%2By%5E2%2F8+=1