SOLUTION: write an equation of each ellipse in standard form with center at the orgin with given characteristics: foci(+-5,0;co vertices(0,+-2)

Question 425331: write an equation of each ellipse in standard form with center at the orgin with given characteristics: foci(+-5,0;co vertices(0,+-2)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write an equation of each ellipse in standard form with center at the orgin with given characteristics: foci(+-5,0;co vertices(0,+-2)
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I believe the statement for the given was written in error. The foci and vertices must both be on the major axis. I believe you meant the major axis to be on the x-axis as the foci is. The points given for the vertices were probably meant to be the end points or the minor axis. My solution will assume the corrected interpretation.
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Standard form for this ellipse:
(x-h)^2/a^2+(y-k)2/b^2=1 (a>b), with (h,k) being the (x,y) coordinates of the center and a horizontal major axis. Since the center is at (0,0) the standard form becomes x^2/a^2+y^2/b^2=1. All we need to do to get the equation is to find a^2.
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a^2=(to be determined)
2b=length of minor axix=4
b=2
b^2=4
c=length of foci=5
c^2=a^2-b^2
a^2=c^2+b^2=25+4=29
a=sqrt(29)=5.39
2a=length of major axis =10.77
Equation:
x^2/29+y^2/4=1
The graph below can serve as a check.
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y=+-(4(1-x^2/29))^.5

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