Exam 14: Parametric Equations and Conic Sections

Write a parameterization of one branch of the following hyperbola using hyperbolic functions :

A mouse hanging on to the end of the windmill blade shown below has coordinates given by , where the origin is at the center of the blades, x and y are in meters, and t is in seconds. The blades are 5 meters long and the windmill makes one complete revolution every 28 seconds in a counterclockwise direction. The mouse starts in the 3 o'clock position and, 10.5 seconds later, loses its hold and flies off. Assume that when the mouse leaves the blade it moves along a straight line tangent to the circle on which it was previously moving. The equation of that line is y = _____ + _____x. Round to 2 decimal places if necessary.

Identify the center and radius of

A satellite moves in an elliptical orbit with the moon at a focus. The nearest it gets to the moon is 1.21 million km and the farthest is 3.6 million km. What is the length of the major and minor axes?

The line between (0,5) and (-1,9) can be parametrized by , ,

Write the ellipse in the form .

Give a parameterization for the vertical line through the point (3,4).

Write a parameterization of one branch of the following hyperbola using hyperbolic functions :

Find the center, vertices, and asymptotes for the following hyperbola :

What is the radius of the circle parameterized by ?

What happens to the graph of the hyperbola as n decreases?

Which of the following is the implicit equation for the ellipse graphed below?

Give a parameterization for the horizontal line through the point (3,-3).

In the hyperbola given by the equations , the asymptote that slopes upward has equation y = _____ x + _____. Round both answers to 2 decimal places.

Parameterize the hyperbola .

a) Parameterize . b) Which t values give the left half of the hyperbola?

Is odd, even, or neither?

Write in terms of and .

A mouse hanging on to the end of the windmill blade shown below has coordinates given by , where the origin is at the center of the blades, x and y are in meters, and t is in seconds. The blades are 3 meters long and the windmill makes one complete revolution every 24 seconds in a counterclockwise direction. The mouse starts in the 3 o'clock position and, 9 seconds later, loses its hold and flies off. How many meters/sec. is the mouse traveling while it is on the blade? Round to 2 decimal places.

Graph .