Question 692187
Find the vertices, foci, and eccentricity of the ellipse. Determine lengths of major and minor axes, and sketch the graph. 
{{xˆ2+4yˆ2=1}}
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Standard form of equation for an ellipse with horizontal major axis:
{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=(x,y) coordinates of center
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Rewrite given equation into standard form: {{{x^2/1+y^2/(1/4)=1}}}
center:0,0)
a^2=1
a=1
length of major axis = 2a=2
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b^2=1/4
b=1/2
length of minor axis=2b=1
see graph below:
y=±(1/4-x^2/4)^.5
{{{ graph( 300, 300, -2, 2, -2, 2,(1/4-x^2/4)^.5,-(1/4-x^2/4)^.5) }}}