parametric equation

Apr 2010
15
0
Show by eliminating the parameter \(\displaystyle \theta \) that the following parametric equations represent a hyperbola:

\(\displaystyle
x = a\tan\theta
\)

\(\displaystyle
y = b\sec\theta
\)

Not really sure how to even start this problem. Any help would be appreciated!
 
Jun 2009
806
275
Show by eliminating the parameter \(\displaystyle \theta \) that the following parametric equations represent a hyperbola:

\(\displaystyle
x = a\tan\theta
\)

\(\displaystyle
y = b\sec\theta
\)

Not really sure how to even start this problem. Any help would be appreciated!
\(\displaystyle x^2 = a^2\tan^2\theta\)

\(\displaystyle y^2 = b^2\sec^2\theta\)

Use the identity \(\displaystyle \sec^2\theta - tan^2\theta = 1\)

Solve the problem.
 
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