Graphing Hyperbolas
The standard equation for a hyperbola can take one of two forms:
( x - h )2 | - | ( y - k )2 | = 1 | with vertices at ( h ± a, k ) or | ||
a2 | b 2 | |||||
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( x - k )2 | - | ( y - h)2 |
| = 1 | with vertices at ( h, k ± b ). | |
a2 | ||||||
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 a hyperbola, consider the “top” and “bottom” halves of the hyperbola as two different parts of the graph because each individual is a function. Solve the equation of the hyperbola for y and enter the two parts in two locations of the Y= list.
Example
Graph a hyperbola in rectangular mode. Solve the equation for y to put it in the standard form.
Graph the hyperbola x 2 + 2x - y 2 - 6y + 3 = 0
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:
ZOOM 
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ENTER 
ALPHA
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Step & Key Operation | Display | Notes |
1Solve the equation for y completing the square.
Enter
Y1 = √ x 2 + 2x + 12 Y2 = Y1
Y3 =
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2nd F 
VARS 
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ENTER 
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ENTER
2nd F 
VARS 
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x 2 + 2x - y 2
x 2 + 2x - (y 2 + 6y + 9) =
(y + 3)2 = x 2 + 2x + 12
y+ 3 = +√ x 2 + 2x + 12 y = +√ x 2 + 2x + 12 - 3
2Turn off Y1 so that it will not graph.
ENTER
