Another way to locate the foci of a hyperbola is by rotating the asymptote rectangle about its center so that opposite corners lie on the line of symmetry that contains the vertices of the hyperbola. From the diagram, you can see that the distance from the origin to a focus is one-half the length of the diagonal of the rectangle.
a. Show that this distance is ˆša2 + b2.
b. Find the coordinates of the foci for (y + 2/1)2 - (x - 2/3)2 = 1.

Transcribed Image Text:

ar