Draw the graph of y = 1/x.
a. Label the vertices of the hyperbola.
b. The x- and y-axes are the asymptotes for this hyperbola. Draw the box between the two branches of the hyperbola that has the asymptotes as its diagonals. The vertices should lie on the box.
c. The dimensions of the box are 2a and 2b. Find the values of a and b.
d. The foci of the hyperbola lie on the line passing through the two vertices. In this case, that line is y = x. The foci are c units from the center of the hyperbola where a2 + b2 = c2. Find the value of c and the coordinates of the two foci.