Parametric equation of a parabola
General Contents
Detailed Contents
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Solve and graph
.
Try to plot this graph without using your graphing calculator. Then check by clicking the “Next” button.
alt="Graph of a parabola. 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?
It looks like part of a parabola.
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 cos(
t
).
From the “
x
”equation, we get
Solve the original equations for sin2(
t
0.
From the “
y
” equation we get
.
Set up the identity and substitute.
.
Solve for y.
We get
Compare this to the general equation of a parabola.
The general equation is
What is the meaning of
A
,
h
, and
k
?
(
h
,
k
) are the coordinates of the vertex of the parabola, and
A
is the amplitude.
Is this consistent with the graph?
Yes, the vertex is at (0,3) and the amplitude is
.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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General Contents
Detailed Contents
Index