Exam 14: Parametric Equations and Conic Sections

Write in terms of powers of e.

P is a point on the unit circle, and Q and R lie on the ellipse shown below. The equation of the ellipse is given by . What is the x-coordinate of R?

The ellipse given by the equation has a height of _____ units and a width of _____ units.

Let . a) Graph the curve. b) Eliminate the parameter to obtain an equation for y as a function of x.

Which of the following are focal points of the ellipse ?

Find the lower intersection point of the ellipse and the line x = -5. Round the y-coordinate to 2 decimal points.

The line between (0,4) and (-3,10) can be parameterized by , ,

The ellipse given by the equations , has a height of _____ units and a width of _____ units.

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, 3 seconds later, loses its hold and flies off. What is A?

Mars moves in an elliptical orbit with the sun at a focus. The closest Mars gets to the sun is 128 million miles and the farthest it gets from the sun is 155 million miles. The length of the major axis is _____ million miles.

In the hyperbola given by the equations , the left vertex is at ( _____, _____ ).

Which of the following sets of equations parameterize the circle ? Mark all that apply.

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

The directrix of the parabola is at y = _____.

Write in terms of and .

is a circle of radius 3 centered at (-3,5)

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 7 meters long and the windmill makes one complete revolution every 20 seconds in a counterclockwise direction. The mouse starts in the 3 o'clock position and, 2.5 seconds later, loses its hold and flies off. What is k? Round to 2 decimal places.

Each end of a string is tacked to the point (2, 0) and (-2, 0) on inch graph paper. The string is 12 inches long. A pencil pulls the string taut and rotates to sweep out an ellipse. What are the focal points of the ellipse?

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

In the ellipse given by the equations , the y-values range from a minimum of _____ to a maximum of _____ about the midline y = _____.