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Question 386103: Find the vertices, foci, and minor axis: (x-1)^2/21 + (y-3)^2/4 = 1
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
Standard Form of an Equation of an Ellipse is 
where Pt(h,k) is the center and vertices are determined by distance of a and b from center
(x-1)^2/21 + (y-3)^2/4 = 1 sqrt(21) = 4.58
center is (1, 3), vertices are (5.58, 3) and (-3.58,3). minor axis is x=1
sqrt(21 - 4) = sqrt(17)= 4.12 Foci are:(5.12,3) and (-3.12,3)
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
That is the form:
because a is always greater than b in an ellipse.
It has center (h,k) = (1,3), semi-major axis = a =  ,
and semi-minor axis = b = 
It has its major axis horizontal because aČ is under the term in x
We plot the center:
We draw the complete major axis  , about 4.6 units right and
left from the center (in green). The endpoints of the major axes are the
vertices. Since the vertices are units right and left of the
center, their coordinates are (1 ± ,3)
We draw the complete minor axis  units above and below
the center (also in green):
We sketch in the ellipse:
Finally we find the foci which are c units from the center and are
located on the major axis, where
 , about 4.1 units.
So the coordinates of the foci are (1 ±  ,3)
I'll plot them. They are just inside the ellipse on each end:
Edwin
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