Answer: The center is (-5,4), the foci are (-5,2), and (-5,6),
and the vertices are (-5,8), (-5,0).
.
Answer: The magnitude is 
, and the direction angle is
approximately 
.
Answer: The equation is 
, if the midpoint on the roadway is chosen as the origin of the coordinate system.
to
rectangular form.
Answer: The rectangular equation is
- Suppose we wish to rotate the axis to eliminate the xy-term.
Find the angle of rotation
. (Use exact values.)
Answer: The angle of rotation
.
- Using your result from above, express x and y in terms of
x' and y'.
Answer:
.
Answer: The two sets of polar coordinates are 
, and
.
, and 
.
- Find the projection of u onto v.
Answer: The projection of u onto v is
.
- Find the vector component of u orthogonal to v.
Answer: The vector component is
.
, and
.
Answer: The equation for the hyperbola is
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.
Answer:
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