Advanced Algebra (Pre-Calculus)
Conics Test Review
Name _________________
Date _________
Show work for each problem. No calculator!
How do you tell whether an equation represents a
circle, parabola, ellipse, or hyperbola?
Discuss the conic whose equation is given.
Then sketch a good graph, showing the key points and lines.
1.] x 2  10 x  8 y  1
y
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Vertex: ________

Focus: __________
x
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Directrix: __________
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Axis of Symmetry: _________
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
Endpoints of Latus Rectum: _________
_________

y

2.] 16  x  4   4  y  2   64
2
2
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x
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Center: ________
Vertices: ______
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_______
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Foci: _______
_______
Length of major axis: ______
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3.] 2 x 2  2 y 2  16 x  20 y  50  0
y
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Center: __________
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Radius: __________
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x-intercept(s): ____________
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x
y-intercept(s): ____________
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----------------------------------------------------------------------------------------------------Determine the equation (in standard form) for each of the conics described below.
Sketch its graph.
_______________ 4.] Parabola with F(-3, 1) and V(-1, 1).
y
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x
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_______________ 5.] Circle with center at (3, -2) and passes through (-1, 1).

y
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x
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_______________ 6.] Ellipse with vertex at (2, 3) and (-4, 3) and focus at (1, 3).
y
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x
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7.] Sketch a graph of the hyperbola whose equation is: 4(x – 1)2 – 16(y-2)2 = 64
Show important points and lines. (C, F, V, Asymptotes)
Also write equation of asymptotes.

y
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

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x
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8.] Discuss the hyperbola: 4x2 – 24x - y2 – 4y = -16.
Then sketch the graph.
y
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x
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9.] Center (-1, 2)
Focus (-5, 2)
Vertex (2, 2)
y

Write an equation and sketch a graph.

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x
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10.] Focus (1, 6); Vertices: (1, -4) and (1, 4)
Write an equation and sketch a graph.

y
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x
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11.] Center (4, 1)
Focus (9, 1)
Vertex (1, 1)
Write an equation and sketch a graph.

y
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
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x
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12.] Vertices: (1, -5) and (1,1)
Asymptote: (y + 2) = 2/3(x – 1).
Write an equation and sketch a graph.
y
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
x
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
13. Write an equation in standard (h, k) form for each conic below.
y
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y
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
x
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x
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

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
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
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
Complete the following equations:
Ellipse: c2 = _________
(a2 is always biggest!)
Hyperbola: c2 = ________ (a2 is always first!)

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