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Write an equation for the ellipse described below:
the endpoints of the major axis are at (10,2) and (-8,2). The foci are at (6,2) and (-4,2).
I have found that the center is at (1,2), but this may be wrong.
Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
The difference between the two forms is the interchange of a^2 and b^2.
Major axis and foci located on the line, y=2, shows that this ellipse has a horizontal major axis, with center at (1,2) as you correctly figured out.
length of major axis=18=2a
See the graph below for a visual check on the answers.