- Find the center, foci, and vertices of the ellipse
Answer: The center is (-5,4), the foci are (-5,2), and (-5,6),
and the vertices are (-5,8), (-5,0).
- Find the magnitude and direction angle of the vector
Answer: The magnitude is , and the direction angle is
- Each cable of a suspension bridge is suspended (in the shape of
a parabola) between two towers that are 480 feet apart and 60 feet
above the roadway. The cables touch the roadway midway between the
towers. Find an equation for the parabolic shape of each cable.
Answer: The equation is , if the midpoint on the roadway is chosen as the origin of the coordinate system.
- Convert the polar equation to
Answer: The rectangular equation is
- Consider the equation
- Find two sets of polar coordinates for the point (-4,3), where
Answer: The two sets of polar coordinates are , and
- Let , and .
- Find an equation for the hyperbola with vertices at (-1,5) and
(-1,1), and with asymptotes , and
Answer: The equation for the hyperbola is
- Follow these instructions carefully: Sketch the graph of
by hand. Have a table of at least
seven appropriate values for r and . Use exact values
for (no decimals). Sketch your graph by plotting the ordered
pairs from your table (use the graph paper below). The shape of the curve must
be apparent from your table of values. If it isn't, you must choose
more appropriate values for . You may use symmetry to avoid
plotting too many points.
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Sun Jul 20 23:05:21 MDT 1997
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