Question 742067
Write an equation for each ellipse described below
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The foci are a (4,0) and (-4,0). Then end points of the minor axis are at (0,2) and (0,-2).
This is an ellipse with horizontal major axis. (x-coordinates of foci change, but y-coordinates do not. Its standard form: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
x-coordinate of center=0 (midpoint of foci)
y-coordinate of enter=0 (midpoint of minor axis)
center: (0,0)
length of minor axis=4=2b
b=2
b^2=4
c=4 (distance from center to foci)
c^2=16
c^2=a^2-b^2
a^2=c^2+b^2=16+4=20
Equation of given ellipse:
{{{x^2/20+y^2/4=1}}}
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The center has coordinated (5,-4). The minor axis is parallel to the x-axis with a length of 6. The major axis has a length of 10.
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Given ellipse has a vertical major axis. Its standard form:  {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (5,-4)
length of major axis=10=2a
a=5
a^2=25
length of minor axis=6=2b
b=3
b^2=9
Equation of given ellipse:
{{{(x-5)^2/9+(y+4)^2/25=1}}}