SOLUTION: find the equation of the ellipse in general form with vertices at (-2,1) and (4,1) with eccentricity of ⅔

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Question 1168621: find the equation of the ellipse in general form with vertices at (-2,1) and (4,1) with eccentricity of ⅔

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
find the equation of the ellipse in general form with vertices at (-2,1) and (4,1) with eccentricity of 2%2F3
the equation of the ellipse in general form:
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
The distance from the center to a vertex is the fixed value a.
e+=+c%2Fa => c%2Fa=2%2F3-> c=2 and a=3
then
b%5E2+=+a%5E2+-+c%5E2
b+%5E2=+3%5E2+-+2%5E2
b%5E2=+9+-+4
b%5E2=+5
b=+sqrt%285%29

so far equation is:

%28x-h%29%5E2%2F9%2B%28y-k%29%5E2%2F5=1
The distance from the center to a vertex is the fixed value a.
Since the vertices of the ellipse are (-2,1) and (4,1) , and a=3 then
(-2%2B3,1)=(1,1)

(4-3,1)=(1,1)
=> h+=+1, k+=+1
and your equation is:
%28x-1%29%5E2%2F9%2B%28y-1%29%5E2%2F5=1