1. Warm Up 1) Verify algebraically whether or not y = 4x + 134 and x(t)= 3.5t - 21, Y(t) = 14t + 50 are the same path. 2) Determine whether or not (186, -268) is a point on the graph of x = 6 + 2t, y = 5 - 3t.

2. Homework Answers…

3. Parametric Equations Day 2

4. Sketching a graph Sketch the curve represented by the parametric equations (indicate the direction using arrows) for -3 < t < 3. Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

5. Creating a parametric equation x = y 2 + 3y

6. Parametric Equations Investigation

7. Along the River Thames in London, England, there is a huge Ferris wheel known as The British Airways London Eye, but often called the Millennium Ferris Wheel. The Wheel is 135 m (just under 450 ft) high and makes one complete revolution every 15 minutes, in a counterclockwise direction, when the ride is underway. For this exploration, we will reduce the immense passenger capsules to mere points on the rim of a circular wheel. The capsules must clear the ground in their rotation, but we will assume that the radius of the Wheel is the full 67.5 m — exactly one-half the height of the Wheel. This will allow our model to reflect ground level access to the capsule for its passengers.

8. Recall the radius of the London Eye Ferris wheel was 67.5 meters. How will this affect the parametric equations for this circle? Also recall that the wheel revolves once every 15 minutes. How far will the wheel rotate in 1 minute? This is the angular velocity and is the coefficient of t in our parametric equations.

9. Let the point (0, 0) correspond to the location of a capsule when it is at ground level and let t = 0 represent the time when a particular capsule is at ground level. Write parametric equations that represent the motion of this capsule on the London Eye over the course of a 15 minute ride. Graph the equations on your calculator in an appropriate viewing window. What are the coordinates of the capsule at the beginning and end of the ride? How high off the ground is the capsule after 10 minutes?