Question 410616: write the equation of the ellipse with foci at (+/-2,0) and x intercepts at +/-5.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write the equation of the ellipse with foci at (+/-2,0) and x intercepts at +/-5.
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Standard form of given ellipse: x^2/a^2+y^2/b^2=1
This is an ellipse with a horizontal major axis on the line, y=0
foci at (-2,0) and (2,0)
so, c=2
c^2=4
x-intercepts are also on line, y=0, which are also the vertex points,(-5,0) and (5,0)
so, a=5
a^2=25
c^2=a^2-b^2
b^2=a^2-c^2
b=sqrt(25-4)=sqrt(21)
b^2=21
Equation of ellipse:
ans:
x^2/25+y^2/21=1
see graph below:
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y=+-((525-21x^2)/25)^.5
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