Parametric equation of a hyperbola
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 hyperbola. 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 a hyperbola.
Along which axis?
Along the
x
-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 secant and tangent both present, we should try that form of the Pythagorean identity.
What is that?
Solve the original equations for sec(
t
).
From the “
x
”equation, we get
Solve the original equations for tan(
t
0.
From the “
y
” equation we get
.
Set up the identity and substitute.
, or
Compare this to the general equation of a hyperbola.
The general equation is
What is the meaning of
a
and
b
?
is the slope of the asymptote in the graph.
Is this consistent with the graph?
Yes, the asymptotes go through (3,2) and (3, – 2).
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