## Equation of an Hyperbola

It may be recalled the equation for an ellipse centered at the origin is,x^{2}/a^{2} + y^{2}/b^{2} = 1

The equation for an hyperbola centered at the origin is very similar,

x^{2}/a^{2} – y^{2}/b^{2} = 1

x^{2} – y^{2} = r^{2}

x^{2} – y^{2} = 1

The red-half and the blue half in the graph are part of the same curve. The green lines are called asymptotes, since the “arms” approach the lines, but never quite reach it. If the equation had been,

y^{2} – x^{2} = 1

## Effects of Adjusting Parameters

If in our equation we increase r, we increase the distance between the halves of the hyperbola. If we adjust put a number in front of the y or the x (or one number before the y and a different number before the x), we change the opening of the two halves of the hyperbola.In addition, there are ways of rotating the curve, and of shoving it to the right or the left or up or down. Still, what we have discussed here should give us a basic understanding of what an hyperbola is.

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