Math 5  Trigonometry  fall ’06  Chapter 6 Test              Name________________________

Show all work for credit.  Write all responses on separate paper.

 

1.      Find an equation for the parabola with vertex at (0,0) and directrix x = 2.  What is the focal diameter?  Construct a careful graph.

2.      Consider the conic described by .

a.       Where are the vertices?  Give coordinates.

b.      Where are the foci?  Give coordinates.

c.       Find the eccentricity.

d.      Write parameteric equations for this conic.

e.       Construct a careful graph showing the key features.

3.      Consider the conic described by .

a.       Where are the vertices?  Give coordinates.

b.      Where are the foci?  Give coordinates.

c.       Write equations for the asymptotes.

d.      Write parameteric equations for this conic.

e.       Construct a careful graph showing the key features.

In 4  6, write an equation for the conic whose graph is shown.

4.     

 

5.

6.

7.      Write in standard form and sketch a graph: 

8.      Write in standard form and sketch a graph:  

 

9.      Write an equation for the hyperbola with foci at  and asymptotes

 

10.  Consider the conic described by  

a.       Use the discriminant to determine whether the graph of this equation is a parabola, and ellipse, or a hyperbola.

b.      Use rotation of axes to eliminate the xy-term in the equation.

c.       Sketch a graph for the equation.

d.      Where are the vertices in the xy coordinate system?

11.  Consider the parametric curve given by
               

a.       Construct a careful graph for the curve.

b.      Eliminate the parameter θ to obtain an equation for this curve in rectangular coordinates.