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Solved Examples
Curriculum:
Alaska Math Grade Level Expectations
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Topic:
Analytical Geometry in Two and Three Dimensions
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Lesson:
M.A.4, C.1: Translation and Rotation of Axes
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Attempt following question by selecting a choice to answer.
c
Choose the angle to which the axes need to be rotated to remove the
x′
y'
terms
in the transformed equation of
11
x
2
+ 2
3
x
y
+ 5
y
2
= 0.
D c
A.
c
π
2
B.
c
π
3
C.
c
π
1
2
D.
c
π
6
c
C
View Solution Steps
Step 1: 11
x
2
+ 2
3
x
y
+ 5
y
2
= 0[Original equation.]
Step 2: A = 11 , B = 2
3
and C = 5[Compare with A
x
2
+ B
x
y
+ C
y
2
= 0.]
Step 3: Let
α
be the angle of rotation needed to eliminate the
x'
y'
term in the transformed equation of the given equation, then cot 2
α
=
A
-
C
B
Step 4:
α
=
1
2
Cot
-1
(
A
-
C
B
)
[Solve for
α
.]
Step 5: =
1
2
Cot
-1
(
1
1
-
5
2
3
)
[Substitute the values of A, B, and C.]
Step 6: =
1
2
Cot
-1
(
3
)
Step 7:
α
=
π
1
2
Step 8: The axes need to be rotated by an angle of
π
1
2
to remove the
x'
y'
- term in the transformed equation.
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