**Answers to MAT 162 Test 2 Sample Questions**

__
Conic__

1.
Determine
what type of conic section is given by the equation _{}. Put the equation in standard form and identify the
important relevant information. Sketch the curve on the grid below.

Hyperbola

Standard form: _{}

center: _{}

vertices: _{}, _{}

foci: _{}, _{}

__Parametric__

2.
Below is shown the curve given parametrically by _{}, _{} over the parameter interval _{}. Clearly label the initial point, the terminal point, and the
points corresponding to _{}, _{}and _{}. Indicate the direction the curve is traced and how many
times the curve is traced (over the interval _{}).

3. Find the Cartesian equation for the curve given in Question #2.

_{}

4.
Find the derivative _{} and the second derivative _{} of the curve given in Question #2.

_{} _{}

5.
Find the (Cartesian) equation of the line tangent to the curve given in
Question #2 at the point corresponding to _{}.

_{}

6.
Write the integral to find the length of one tracing of the entire curve
given in Question #2. *(Note: You do not need to evaluate the integral.)*

* *

_{}

7.
Write the integral to find the area inside the curve and **below** the
*x*-axis, and evaluate this integral.

_{}

8.
Write the integral to find the surface area of the solid generated by
revolving the region in Question #7 around the *x*-axis. *(Note: You do
not need to evaluate the integral.)*

_{}

9.
Write the integral to find the volume of the solid generated by revolving
the region in Question #7 around the *x*-axis. *(Note: You do not need to
evaluate the integral.)*

_{}

10.
Plot the point _{} on the polar grid below. (Label the initial ray, and include
a scale with your plot.) Find two additional representations of this same point,
one with r > 0 and one with r < 0. *(Note: angles which reduce to _{}are not considered to be different from *

_{}

*Note: there
are many others *

11.
Below
is shown the curves given by _{} and _{}. Identify which curve is which. Plot and label the points
corresponding to _{} and _{} on the curve given by _{}.

12.
Find the derivative _{} of _{}.

_{}

13.
Find the (Cartesian) equation of the line tangent to the curve given by
_{} at the point where _{}.

_{}

*
14.
*Set up the integral to find
the length of one tracing of _{}. *(Note: You do not need to evaluate the integral.)*

_{}

15.
Set up the integral to find the area of the region inside the curve given
by _{} and outside the curve given by _{}. *(Note: You do not need to evaluate the integral.)*

_{}

16.
Set up the integral to find the area of the region inside both curves
(where they overlap) _{} and _{}, and evaluate this integral.

_{}