CHAPTEB
CHAPTER
8 ANALYTIC GEOMETRY
8 PRACTICE TEST
)
For the following exercises, write the equation in standard form
and state the center, vertices, and foci.
r.t+'=r
g 4
9t' + t6x, _
Z,
36y
+ 32x g2_O
For the following exercises, sketch the graph, identifying the
center, vertices, and foci.
 (x3)' (v
5'
2tt
write the standard form eguation ofan ellipse with
center at ( I, 2 ), vertex at (7' 2), and focus at (4,
2).
a
6.
A whispering gallery is to be constructed with a
tengtrr of tso feet. ti the foci are to be located 20 feet
away from the wall, how high should the ceiling be?
For the follorving exercises, write the equation of the hyperbola in standard
form, and give the center, yertices, foci,
and asymptotes.
x2
t'l
49
8t
8. 16.}.

9xr
!
12q, + I12 =
0
For the following exercises, graph the hyperbola, noting its center, vertices,
and foci. State the e quations of the
asymptotes.
s.(x3)'_(y+31'z_l
25
11.
10.
I
y'
x'z+
4y
,lx
 18:0
Write the standard form equation ofa hlperbola
with foci at ( I, 0) and ( l, 6), and a vertex at (1, 2).
For the following exercises, write the equation of the parabola in standard
form, and give the vertex, focus, and
equation of the directrix.
12.
f + llx 0
13.3x,

tzx _ y
+ 1t:O
For the follorving exercises, graph the parabola, labeling the vertex,
focus, and directrix.
14.(x16'
1)r a0+ 3)
r5.y.+8x_ 8/+40_0
write the equation ofa parabora with
(2, 3) and directrix
7
:  l.
a focus
at
17.
A searchright is shaped like a paraboloid of
revolution. Ifthe light source is located 1.5 feet from
the base along the axis of symmetry, and the depth
ofthe searchlight is 3 feet, what should the width of
the opening be?
For the following exercises, determine which conic section is represented
by the given equation, and then determine
the angle I that will eliminate the xy term.
18,3x'

2xy
+ 3Y :4
19.
x, + 4xy +
For the following exercises, rewrite in the ri'system without the
tx]+tO\/1xy+y.:4
bl
+ 6r
 81:
Q
.ri'term, and graph the rotated graph
21, 16x'z
+ 244r +
9f 
t25x =
O
or the following exercises, identify the conic with focus at the origin, and
then give the directrix and eccentricity.
22.
2sind
4+ 6cosj
For the following exercises, graph the giyen conic section.
an ellipse or a hyperbola, label vertices and foci.
24
r:
12
4 gsing
Ifit
is a parabola, label vertex, focus, and directrix.
2
25'l:4+4sino
25. Find a polar equation of the conic with focus at the
origin, eccentricity ofe 2, and directrix:
3.
:
x:
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