SOLUTION: E is the ellipse with foci at (4,−2) and (4,8) and whose major axis has length 20.

Question 1037746: E is the ellipse with foci at (4,−2) and (4,8) and whose major axis has length 20.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
So, that is E, but what is the question?
Write the equation?
Locate vertices and co-vertices?
graph?

Both foci are on the vertical line ,
so this is an ellipse with foci and vertices on the vertical major axis .
The center is the midpoint of the segment connecting the foci.
That is point (4,3), with coordinates
and
the averages of the foci coordinates.
The focal distance, , is the distance from one focus to the center:
.
Since the major axis has length ,
the semi-major axis is .
Since the major axis is vertical, the vertices of the ellipse are units above and below center (4,3), at (4,-7) and (4,13).
The semi-minor axis, , can be calculated using the relation
.

100-9=b^2}}}

The equation of an ellipse with major axis parallel to the y-axis,
center at point (h,k), is

In this case, with ,
the equation is
.
The co-vertices are on the horizontal minor axis,
a distance to the left and rihjt of center (4,3),
at

and

.
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SOLUTION: E is the ellipse with foci at (4,&#8722;2) and (4,8) and whose major axis has length 20.

SOLUTION: E is the ellipse with foci at (4,−2) and (4,8) and whose major axis has length 20.