Ellipses Answers to Question 1-6
1. 
Because 
is an axis of symmetry
.
Thus,
.
In summary we can say that 
the length of the major axis.
2. 
Recalling
that 
and 
cm
We
can conclude that 
and
.
Thus they are each equal to 5.695 cm.
3.
Recall that 
5.695 cm and 
4.27 cm.
Using the Pythagorean Theorem
. Plugging in values
and solving for
, is approximately
3.767305.
4.
Recall that
,
Thus 
This is
commonly written as 
where
.
a = half the length of the major axis and b = half the length of the minor axis.
- Using what was derived in problem number
four,
, and plugging in the values for 
and 
the foci are located approximately 3.768 cm right of the center
of the ellipse and 3.768 cm left of the center of the ellipse.
- Students should realize that is easy to locate the
foci using a compass only. A circle
should be constructed with
as the center and
- segment as the radius.
The intersections of the circle and segment
are where the
foci are located. See picture
below.
