Graphing Ellipses (Math Worksheet)
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1
2EL-9900 Graphing Calculator
Graphing Ellipses
The standard equation for an ellipse whose center is at the point (h, k) with major and
(x - h)
2
2
(y - k)
minor axes of length a and b is
+
= 1.
2
a
2
b
There is a problem entering this equation in the calculator graphing list for two reasons:
a) it is not a function, and only functions can be entered in the Y = list locations.
b) the functions entered in the Y = list locations must be in terms of x, not y.
To draw a graph of an ellipse, consider the “top” and “bottom” halves of the ellipse as two
different parts of the graph because each individual is a function. Solve the equation of the
ellipse for y and enter the two parts in two locations of the Y = list.
Example
Graph an ellipse in rectangular mode. Solve the equation for y to put it in the
standard form.
2
2
Graph the ellipse 3(x -3)
+ (y + 2)
= 3
Before
There may be differences in the results of calculations and graph plotting depending on the setting.
Starting
Return all settings to the default value and delete all data.
Set the zoom to the decimal window:
A
(
)
ZOOM
ENTER
ALPHA
7
Step & Key Operation
Display
Notes
1
Solve the equation for y, completing
3(x - 3)
2
+ (y + 2)
2
= 3
the square.
2
2
(y + 2)
= 3 - 3(x - 3)
Enter
√
+
y + 2 =
3 - 3(x - 3)
2
√
Y1 =
3 - 3(x - 3)
2
√
+
2
y =
3 - 3(x - 3)
- 2
Y2 = Y1 - 2
Y3 = -Y1 -2
√
—
(
Y=
3
3
2nd F
x
n
—
)
3
2
X/ /T/
ENTER
—
A
1
2nd F
VARS
ENTER
-
(
)
2
ENTER
2nd F
VARS
ENTER
—
1
2
2
Turn off Y1 so that it will not graph.
ENTER
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