![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
(a)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=dd40ab2e6484f4ddb48c55934d6c669b.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e209f4963d8db1522f438c0a24dc29f3.png\")
.
Find the rectangular equation.
\Consider ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=dd40ab2e6484f4ddb48c55934d6c669b.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=cb831915ef9c9c4d6637512c7aaf3b26.png\")
Substitute ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=cb831915ef9c9c4d6637512c7aaf3b26.png\")
in ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e209f4963d8db1522f438c0a24dc29f3.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c3c3d3ada9b3af4875a1054540c9b89a.png\")
The rectangular equation is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c3c3d3ada9b3af4875a1054540c9b89a.png\")
.
Graph:
\Graph the parametric equations and .
![\"\"](\"/userfiles/48-718-36a.gif\")
.
Observe the graph:
\The domain of the graph is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a884b3c3c4acc19dc1398473286275c3.png\")
.
The orientation is towards up and curve is smooth and continuous.
\The range is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9de658e7fcac17bc1614c5528fce227c.png\")
.
![\"\"](\"/userfiles/image/steps_images/step2.JPG\")
(b)
\The parametric equations are ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c59ec81a9166242b1b08f54fefef7e98.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=f74a0434c0d7d531e1452fbd417dc247.png\")
.
Graph:
\Graph the parametric equations ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c59ec81a9166242b1b08f54fefef7e98.png\")
and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=f74a0434c0d7d531e1452fbd417dc247.png\")
.
![\"\"](\"/userfiles/48-718-36b.gif\")
.
Observe the graph:
\The domain of the graph is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a884b3c3c4acc19dc1398473286275c3.png\")
.
The orientation is towards down and curve is smooth and continuous.
\The range is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9de658e7fcac17bc1614c5528fce227c.png\")
.
Observe the set of graphs of parametric equations:
\The parametric equations from (a)-(b) are similar and their rectangular equation is .
The curves are identical but orientation is opposite to each other.
\![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
The parametric equations from (a)-(b) are similar and their rectangular equation is .
The curves are identical but orientation is opposite to each other.
\(a)
\The domain of the graph is .
The orientation is towards up and curve is smooth and continuous.
\The range is .
(b)
\The domain of the graph is .
The orientation is towards down and curve is smooth and continuous.
\The range is .