a.

 The hyperbola equation is .

Rewrite the equation as .

Compare the above equation with standard form of hyperbola with horizontal transverse axis is .

and .

Center : ,

Vertices : ,

Foci : ,

Asymptotes : .

Graph the center, vertices, foci, and asymptotes.

The hyperbola equation is .

Solve for .

Make a table of values to sketch the hyperbola.

 The hyperbola equation is .

Rewrite the equation as .

Compare the above equation with standard form of hyperbola with vertical transverse axis is .

and .

Center : ,

Vertices : ,

Foci : ,

Asymptotes : .

Graph the center, vertices, foci, and asymptotes.

The hyperbola equation is .

Solve for .

Make a table of values to sketch the hyperbola.

Graph :

Draw a coordinate plane.

Plot the points obtained in the tables.

Sketch the hyperbolas in the same window.

b.

Analyze .

Vertices : .

Foci : .

Equations of asymptotes : .

 Analyze .

Vertices : .

Foci : .

Equations of asymptotes : .

Comparing the two hyperbolas, the foci are the same value, but the first graph are horizontal and the second graph, the foci are vertical.

The vertices are close together for the first graph.

However, the asymptotes are the same for both graphs.

c.

To write an equation for the conjugate hyperbola , switch the order of the -and -terms : .

d.

The new hyperbolas are and .

Graph :

Draw a coordinate plane.

Graph the hyperbolas in the same window.

e.

Conjugate hyperbolas have the same asymptotes. Also, the distance from the center to each focus is the same.

a.

Graph :

b.

Two hyperbolas, the foci are the same value, but the first graph are horizontal and the second graph, the foci are vertical.

The vertices are close together for the first graph.

However, the asymptotes are the same for both graphs.

c.

.

d.

Graph :

e.

Conjugate hyperbolas have the same asymptotes. Also, the distance from the center to each focus is the same.