SOLUTION: Find an equation of an ellipse having the given intercepts: x - intercepts: +-Square root 6 y - intercepts: +-2Square root 3

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Question 617399: Find an equation of an ellipse having the given intercepts:
x - intercepts: +-Square root 6
y - intercepts: +-2Square root 3
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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x - intercepts: ±Ö6
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y - intercepts: ±2Ö3
Plot those 4 intercepts:

 draw the ellipse 

Since it looks like this: "drawing%2815%2C25%2C-1%2C1%2C-2%2C2%2Carc%28.58%2C0%2C2%2C4%29%29" 
and not like this:"drawing%2825%2C15%2C-2%2C2%2C-1%2C1%2Carc%28.56%2C0%2C4%2C2%29%29",

its equation is

%28x-h%29%5E2%2Fb%5E2 + %28y-k%29%5E2%2Fa%5E2 = 1

The center is (h,k) = (0,0), so it has the form

%28x-0%29%5E2%2Fb%5E2 + %28y-0%29%5E2%2Fa%5E2 = 1

x%5E2%2Fb%5E2 + y%5E2%2Fa%5E2 = 1

The y-intercepts are the vertices, the x-intercepts are the covertices:
                                                               _
a = semi-major axis = distance between center and a vertex = 2Ö3

Therefore 
                                                                _
b = semi-minor axis = distance between center and a covertex = Ö6
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Therefore a² = (2Ö3)² = 4·3 = 12,  b² = (Ö6)² = 6

x%5E2%2F6 + y%5E2%2F12 = 1

Edwin