You may remember that for an ellipse, the foci are inside the closed curve of the ellipse. The hyperbola, however, is a pair of open curves that face outward from the center. The foci are within the curves, but outside the rectangle which is sketched to graph the hyperbola. Note: F1 and F2 in the figure below.

graph of hyperbola with foci at point (-2.8,0)and (2.8,0)

How do you find the location and coordinates of the foci of the hyperbola?

You must find the focal radius by using the following formula:

(major radius)2 + (minor radius)2 = (focal radius)2

In the figure above, both the major radius and the minor radius are 2 units, so:

22 + 22 = (focal radius)2 = 8 therefore, the = focal radius = √8 ˜ 2.8

This is the distance along the major axis (horizontal in this case) from the center to each focus.

So, what are the coordinates of the foci for the graph above?

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(2.8, 0) and (-2.8, 0)Close Pop Up