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Pre-AP Algebra II – Chapter 7 Test Review
Standards/Goals:
 G.GPE.1.: I can identify and recognize the properties of the conic sections
 I can determine the domain of a conic section
 I can identify a conic section by its graph.
 I can derive the equation of a circle
 I can derive the equation of a circle when given the center and radius using the
Pythagorean Theorem
 I can derive the equation of a circle by completing the square to find both the center
and the radius.
 I can derive the equation of a parabola
 G.GPE.2: I can derive the equation of a parabola given a focus and a directrix.
 I can derive the equation of an ellipse
 I can derive the equation of an ellipse, given its foci.
 I can recognize the fact that the sum or differences of the distances from the foci is
constant.
 I can derive the equation of a hyperbola.
 I can derive the equation of a hyperbola using the foci.
 I can translate a conic section by moving its center from (0, 0) to (h, k)
EXAMPLES:
1. What are the lines of symmetry of the following conic sections with the center at the
origin?
a. Ellipse
b. Circle
2. What is an equation of the parabola with the vertex at the origin and focus (0, 3)?
3. Which is an equation of the circle at the origin and radius 12?
4. What is the equation for the translation 𝑥 2 + 𝑦 2 = 16 eighteen units right and
THREE units DOWN?
5. What is the equation for the translation 𝑥 2 + 𝑦 2 = 16 twelve units right and FOUR
units UP?
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6. A hyperbola has vertices (±2, 0) and one focus at (3, 0). What is the equation of the
hyperbola in standard form?
(𝑥 − 5)2
7. A horizontal ellipse has the equation
25
+
(𝑦 − 7)2
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8. What are the foci of the hyperbola with the equation
= 1.
(𝑦 − 1)2
16
Which is a vertex?
−
(𝑥 −8)2
256
= 1?
9. What is the vertex and directrix of the parabola with the equation:
(𝑦 + 5)2 = 5(𝑥 − 7)
10. Identify the INTERCEPTS of each conic section. Additionally, give the DOMAIN and RANGE of
each graph.
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11. A carpenter wants to cut a template for an elliptical window with 2 major axes of 10 ft. and a minor
axis of 6 ft. He has a 10-ft by 3-ft rectangular piece of plywood. The carpenter plans to use a string to
draw the top half of the ellipse, using a nail at each focus. The nails are along the bottom edge, 1 ft
from each end.. What length of string should the carpenter use to sketch the curve?
12. Identify the conic section represented by each equation by writing the equation in
standard form. For a parabola, give the vertex, focus, and directrix. For a circle, give the
center and the radius. For an ellipse or a hyperbola, give the center, vertices and the foci.
Sketch the graph.
#1. 𝑥 2 + 𝑦 2 + 6𝑥 − 10𝑦 = −5
#2. x2 – y + 6x + 8 = 0
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#3. 4x2 + 9y2 – 24x – 36y + 36 = 0
#4. 4x2 – y2 + 24x – 6y + 23 = 0