Version 083 – DGQ06 – gilbert – (55485)
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001
10.0 points
Which one of the following conic sections
has graph
1
2
3
4

1

2
1
2

1

2

3

4
1.
9
x
2

18
x

4
y
2

8
y
= 41
2.
4
x
2

8
x
+ 9
y
2
+ 18
y
= 23
correct
3.
4
x
2

8
x
+ 9
y
2

18
y
= 23
4.
9
x
2
+ 18
x

4
y
2

8
y
= 41
5.
9
x
2

18
x

4
y
2
+ 8
y
= 41
6.
4
x
2
+ 8
x
+ 9
y
2
+ 18
y
= 23
Explanation:
The graph is a shifted ellipse centered at
(1
,

1) whose major axis has length 6 and
minor axis has length 4.
Thus one equation
for this ellipse is
(
x

1)
2
9
+
(
y
+ 1)
2
4
= 1
,
which after expansion and simplification can
be rewritten as
4
x
2

8
x
+ 9
y
2
+ 18
y
= 23
.
keywords:
graph,
conic
section,
ellipse,
shifted ellipse
002
10.0 points
Find the
x
intercept of the tangent line
at
P
(3
,
1) to the graph of the curve defined
parametrically by
x
(
t
) = 6 cos 2
t ,
y
(
t
) = 2 sin
t .
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 Spring '07
 TextbookAnswers
 Parametric equation, Conic section

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