```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




Vertex: ________

Focus: __________
x












Directrix: __________

Axis of Symmetry: _________


Endpoints of Latus Rectum: _________
_________

y

2.] 16  x  4   4  y  2   64
2
2


x





Center: ________
Vertices: ______

_______


Foci: _______
_______
Length of major axis: ______










3.] 2 x 2  2 y 2  16 x  20 y  50  0
y





Center: __________



x-intercept(s): ____________

x
y-intercept(s): ____________












----------------------------------------------------------------------------------------------------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





x














_______________ 5.] Circle with center at (3, -2) and passes through (-1, 1).

y


x


















_______________ 6.] Ellipse with vertex at (2, 3) and (-4, 3) and focus at (1, 3).
y






x











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









x






















8.] Discuss the hyperbola: 4x2 – 24x - y2 – 4y = -16.
Then sketch the graph.
y







x























9.] Center (-1, 2)
Focus (-5, 2)
Vertex (2, 2)
y

Write an equation and sketch a graph.









x





















10.] Focus (1, 6); Vertices: (1, -4) and (1, 4)
Write an equation and sketch a graph.

y






x



















11.] Center (4, 1)
Focus (9, 1)
Vertex (1, 1)
Write an equation and sketch a graph.

y







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





x
























13. Write an equation in standard (h, k) form for each conic below.
y

y





x















x


















Complete the following equations:
Ellipse: c2 = _________
(a2 is always biggest!)
Hyperbola: c2 = ________ (a2 is always first!)









```