Exam 14: Parametric Equations and Conic Sections

Describe the graph of the parametric equations .

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

Parameterize the ellipse centered at the point (-3, 4) with horizontal axis of length 4 and vertical axis of length 6.

is a circle of radius 4 centered at (4,-3).

Parameterize the circle of diameter 5 centered at (3,-4) traversed counterclockwise starting at

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

What is the upper focal point of the ellipse ? Where necessary, round to 2 decimal places.

Parameterize the ellipse so that the parameterization starts at the point (2,2) and travels clockwise.

Write in terms of e.

Find the equation of a parabola centered at the origin with focal point (0, -2).

Answer the following for the hyperbola : a) What is the center? b) Does the hyperbola open left-right or up-down? c) What are the values of a and b?

Rewrite the equation in the form or

Could the graph below be the graph of the parametric equations ? Assume the parameter is restricted to values for which the functions are defined.

Is (0, 2) a vertex of the hyperbola shown below?

If the ellipse is written in standard form , then h = _____, k = _____, a = _____, and b = _____.

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

Parameterize the hyperbola .

Answer the following for the hyperbola : a) What is the center? b) Does the hyperbola open left-right or up-down? c) What are the values of a and b?

A circle centered at the origin also includes the point (4, 6). What is the radius of the circle? Round to 2 decimal places.

Which of the following are focal points of the hyperbola ?