Exam 14: Parametric Equations and Conic Sections

Write in terms of powers of e.

Graph .

Let and parameterize a circle, with a < 0, b > 0, k < a, and k < b. What quadrant does the circle lie in?

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

What is the focus of the parabola ?

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

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 an asymptote of the hyperbola shown below?

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

Does parameterize the ellipse graphed below, traversed in the clockwise direction and starting at the point (-1, -2)?

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

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

Write an implicit equation for the hyperbola that opens left/right whose asymptotes are the diagonal lines through the corners of a rectangle of width 6 and height 8 centered at the point (-3, -5).

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

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

If the circle is put into standard form , then h = _____, k = _____, and r = _____.

What is the center of the hyperbola ?

Write as for some a, b, and c.

What is the explicit formula for the curve ?

What is the explicit formula for the curve ?