Graphing Ellipses
The standard equation for an ellipse whose center is at the point (h, k) with major and
| (x - h) 2 | (y - k) 2 | |||
minor axes of length a and b is | a 2 | + |
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b 2 | |||||
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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.
Graph the ellipse 3(x
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| A | ( | ENTER |
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1Solve the equation for y, completing the square.
Enter
Y1 = √ 3 - 3(x - 3)2 Y2 = Y1 - 2
Y3 =
Y= |
| 2nd F |
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| √ | 3 |
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X/ /T/n |
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2nd F 
VARS 
A 
ENTER 
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2 
ENTER 
2nd F 
VARS 
ENTER
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2
2Turn off Y1 so that it will not graph.
3(x - 3)2 + (y + 2)2 = 3 (y + 2)2 = 3 - 3(x - 3)2
y+ 2 = +√ 3 - 3(x - 3)2 y = + √ 3 - 3(x - 3)2 - 2
ENTER
