Parametric Equations

Eliminate the parameter from the parametric equations:

x = t² + 5 and y = t² - 4.

The graph of the resulting rectangular equation is which of the following?

• Line

• Parabola

• Circle

• None of These

Write the rectangular equation for the following parametric equations.

x = 4cosθ

y = 3sinθ^

• $\frac{x^2}{9}+\frac{y^2}{16}=1$

• $\frac{y^2}{9}+\frac{x^2}{16}=1$

• $\cos^2\theta+\sin^2\theta=1$

• $\frac{x^2}{9}-\frac{y^2}{16}=1$

Sketch the curve of x = 2t + 1 and y = t² + 2.

• A

• B

• C

• D

Eliminate the parameter from the parametric equations:
 $x=2\cos\theta\ \ \ and\ \ \ \ y=2\sin\theta$  
The graph of the resulting rectangular equation is which of the following?

• Line

• Parabola

• Circle

• None of These

The parametric equations for a projectile are given by:
 $x=\left(v_0\cos\theta\right)t\ \ \ \ and\ \ \ \ y=h+\left(v_0\sin\theta\right)t\ -16t^2$  

A football is thrown with an initial velocity of 30 feet per second at a launch angle of  $15\degree$  .  Find the height of the football when it is 25 feet from the quarterback.  Assume the ball is thrown from the quarterback's height, which is 6 feet.
  

• 0.78 feet

• 0.863 feet

• 0.243 feet

• None of These