# parametric equation

#### kevin11

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!

#### sa-ri-ga-ma

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.

kevin11