Hyperbola |
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A hyperbola is a set of all points on a plane where the absolute value of the difference of the distances between two fixed points (the foci) is constant. |

Below we have a graph of a hyperbola:

Figure 1. |
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Its vertices are at (0, 2) and (0, -2). Its center is at (0, 0):

Figure 2. |
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It has a traverse axis, and a conjugate axis:

Figure 3. |
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It also has two diagonal asymptotes:

Figure 4. |
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Equation of an Hyperbola |
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The equation for a hyperbola depends on if it is horizontal or vertical (as determined by its traverse axis). |

Let's find the equation of our hyperbola.

"c" is equal to the distance of each foci from the center.

Figure 5. |
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"a" is equal to the distance of each vertex to the center.

Figure 6. |
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The Pythagorean Theorem can be used in this situation to determine the missing "b" value.

Figure 7. |
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Now, we plug in our a squared, b squares, and center values to have a final equation for our specific Hyperbola:

Figure 8. |
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