General Contents
Detailed Contents
Index
Programmed tutorial: Ellipse: Determine its Equation from a Graph: Example 1
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Find the equation of the ellipse in this diagram. Also determine the foci.
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General Contents
Detailed Contents
Index
First state the standard equation for an ellipse with a horizontal major axis.
What is the interpretation of
h
and
k
?
They give the coordinates of the center of the ellipse.
Determine the coordinates of the center of this ellipse.
The center is at ( 4, 1).
Determine
h
and
k
.
h
=
4;
k
=
1
How is
a
related to the ellipse?
a
is half the length of the major (long) axis.
What is the name of this half of the major axis?
It is the semimajor axis.
a
is its length.
Determine the length of the major axis from the graph.
The axis extends from
x
=
7 to
x
=
1.
Its length is ( 1
)
( 7)
=
6
Determine
a
.
Determine
b
in a similar way.
The minor axis extends from
y
= 3 to
y
= 1.
Hence the semiminor axis is
Substitute these results into the standard equation.
We get
Simplify this equation.
Now determine the locations of the foci.
Which axis are they located on?
They are on the major axis.
Where are they located in terms of
a, b, h, k
?
The center is at (
h, k
).
The foci are a distance c from the center.
Determine
c
.
Determine the
x
-coordinate of the foci.
The
x
-coordinate of the foci are given by
h
±
c
=
4 ± 2.2 = 6.2 or 1.8
Determine the
y
-coordinate of the foci.
They lie on the axis, so their
y
-coordinate is
k
= 1.
State these locations in (
x, y
) form.
The foci are at ( 6.2, 1) and ( 1.8, 1).
Add the foci to the diagram of the ellipse. Then click "Next" to check.
Note the distances
a, b,
and
c
in the diagram.
alt="Java applet graph of a hyperbola, foci, vertices, asymptotes." Your browser is completely ignoring the <APPLET> tag!
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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