Question 606824
Equation (in graphing form) for ellipse with foci points (5,4) and (-3,4) and the major axis is 10 units long.
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Ellipse has a horizontal major axis.
Its equation in 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=(5-3)/2=1 (use midpoint formula and data from given foci)
y-coordinate 0f center=4
center: (1,4)
Given length of horizontal major axis=10=2a
a=5
a^2=25
..
2c=8 (-3 to 5)
c=4
c^2=16
..
c^2=a^2-b^2
b^2=a^2-c^2=25-16=9
b=3
..
Equation of given ellipse:
(x-1)^2/25+(y-4)^2/9=1
see graph below:

..
y=±(9-9(x-1)^2/25)^.5+4


{{{ graph( 300, 300, -10, 10, -10, 10,(9-9(x-1)^2/25)^.5+4,-(9-9(x-1)^2/25)^.5+4) }}}