Parametric equation of an ellipse
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If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
Solve and graph
.
Try to plot this graph without using your graphing calculator. Then check by clicking the “Next” button.
alt="Graph of an ellipse. Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is completely ignoring the <APPLET> tag!
What does this look like?
An ellipse.
Along which axis?
Along the
y
-axis.
Let’s determine the rectangular equation of this graph. How do we proceed when the parametric equations contain trig functions?
Sometimes we can solve for the trig functions (not for
t
itself) and make use of trig identities.
What trig identity could we try here?
When we have sine and cosine both present, we should try the Pythagorean identity.
What is that?
Solve the original equations for sin(3
t
).
From the “
x
”equation, we get
Solve the original equations for cos(3
t
0.
From the “
y
” equation we get
.
Set up the identity and substitute.
.
Is this consistent with the graph?
Yes.
What is the length of the semi-major axis?
The length is 8, or the major axis is 16 units long.
Which axis does it lie on?
The
y
-axis.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
General Contents
Detailed Contents
Index