Test 4 | Time: 1.5 hours |
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- 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 approximately . - 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
rectangular form.

**Answer:**The rectangular equation is - Consider the equation
- 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:**

- Suppose we wish to rotate the axis to eliminate the xy-term.
Find the angle of rotation . (Use exact values.)
- Find two sets of polar coordinates for the point (-4,3), where
.

**Answer:**The two sets of polar coordinates are , and . - Let , 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 .

- Find the projection of
- 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.

**Answer:**

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