Name__________
Period__________
Date___________
Take-home ½-Test on Chapter 8 for Pre-Calculus
Worth 50 points.
The rules:
1. These question are NOT appear on the Internet.
2. At least some work must be shown for all the questions except question 1.
3. No one can do these problems for you.
4. You can ask me for help.
5. You can work with others students in the class
6. Anyone else who would help you must follow the above rules, and be qualified to help.
At the end of this take-home portion will be a place for someone (such as a tutor or
parent) to identify themselves and their qualifications to offer assistance.
7. A calculator may be used on all the questions on this take-home ½-test. However, as
stated in 2 above, at least some work must be shown on all questions (again except
question 1). Also note #8 below:
8. Answers should be given in simplified radical form, not decimals.
9. Attach any scrap paper and/or graph paper you use.
10. Take a good look at the given grids to graph on; they are not all to the same scale.
Problems:
1. (worth 2 points) Identify the conic section from its equation:
a. 𝑦 2 − 3𝑥 + 12𝑦 = 10
(i)
Circle
(ii) Parabola
(iii) Ellipse
(iv) Hyperbola
(iii) Ellipse
(iv) Hyperbola
b. 7𝑥 2 + 14𝑥 + 3𝑦 2 − 18𝑦 − 1 = 0
(i)
Circle
(ii) Parabola
Name__________
Period__________
Date___________
2. (worth 8 points) Given the parabola 𝑥 2 = 36𝑦 determine the following. Then, sketch the
parabola using the endpoints of the focal diameter. Also fill in the requested information
about this conic section.
Focus (in ordered pair form): ______________
Directrix (give an equation): __________
Endpoints of the Focal Diameter (in ordered pair
form): are:
_______________ and _______________
Direction of Opening: ________________
Name__________
Period__________
Date___________
3. (worth 8 points) Given the parabola (𝑦 + 5)2 = −16(𝑥 − 3) determine the following.
Then, sketch the parabola using the endpoints of the focal diameter. Also fill in the
requested information about this conic section.
Focus (in ordered pair form): ______________
Directrix (give an equation): __________
Endpoints of the Focal Diameter (in ordered pair
form): are:
_______________ and _______________
Direction of Opening: ________________
Name__________
Period__________
Date___________
4. (worth 8 points) Find the equation of the ellipse (in standard form), give the requested
information and sketch given:
y
10
Vertices: (–2, –6), (–2, 4)
Foci: (–2, –3), (–2, 1)
a=
b=
c=
x
-10
10
-10
The equation of the ellipse is _____________________.
5. (Worth 8 points) Sketch the ellipse. State exact values for the foci and the vertices of the
major axis and the vertices of the minor axis. Give these answers in ordered pair form.
𝒙𝟐 (𝒚 + 𝟏)𝟐
+
=𝟏
𝟗
𝟒𝟗
y
10
Foci: ____________________
Vertices of the Major Axis are:
x
-10
_______________ and _______________
10
Vertices of the Minor Axis are:
_______________ and _______________
-10
Name__________
Period__________
Date___________
6. (worth 8 points) Determine the following for the hyperbola, and graph:
144𝑥 2 − 4𝑦 2 = 144
Foci (in ordered pair form):
____________________
Vertices (in ordered pair form) are:
_____________ and _____________
Equation of the asymptotes:
______________________________
Name__________
Period__________
Date___________
7. (worth 8 points) Determine the following for the hyperbola, and graph:
4𝑥 2 − 81𝑦 2 + 40𝑥 − 162𝑦 − 305 = 0
Foci (in ordered pair form):
____________________
Vertices (in ordered pair form) are:
_____________ and _____________
Equation of the asymptotes:
______________________________
Name__________
Period__________
Date___________
Bonus questions:

worth 4 points each

no partial credit will be given

some work must be shown to receive credit

For each of the three questions, both parts of the question must be correct to receive
credit.
A) Find the equation of the parabola in standard form, and give the equation of the directrix:
𝑦 2 − 50𝑦 + 8𝑥 − 7 = 0
Equation of parabola: ____________
Equation of directrix: ____________
B)
Find the equation of the ellipse in standard form, and give the coordinates of the vertices
of the major axis in ordered pair form:
𝑦 2 − 20𝑦 + 8𝑥 2 − 128𝑥 = −36
Equation of ellipse: _____________
Coordinates of vertices: __________
C) Find the equation of the hyperbola in standard form, and give the equations of the
asymptotes:
𝑦 2 − 2𝑦 − 12𝑥 2 − 240𝑥 = 4655
Equation of hyerbola: ____________
Equations of asymptotes: _________
I certify that I, ___________, have helped student ___________ without doing these problems
for them. I am qualified to help because of the following credentials:
______________________________________________________________________________