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Oed Long Quiz 1

1. The document discusses conic sections, rotated coordinate systems, and finding coordinates after a rotation. It provides examples of rotating axes to eliminate xy-terms and writing equations in standard form. It also gives problems about finding coordinates after a rotation by a given angle and constructing a room with a semi-elliptical dome ceiling.

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Wayne James Russel
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1K views2 pages

Oed Long Quiz 1

1. The document discusses conic sections, rotated coordinate systems, and finding coordinates after a rotation. It provides examples of rotating axes to eliminate xy-terms and writing equations in standard form. It also gives problems about finding coordinates after a rotation by a given angle and constructing a room with a semi-elliptical dome ceiling.

Uploaded by

Wayne James Russel
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

A type of Conic where the plane is tilted and intersects only on one cone to form a
bounded curve.

Ans:

2. Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard
form. Sketch the graph of the resulting equation, showing both sets of axes.
a. 3𝑥 2 − √3𝑥𝑦 + 𝑦 2 + 2𝑥 + 2√3𝑦 = 0
Ans:
3. The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system. The
coordinates of a point in the xy-coordinate system are given. Find the coordinates of the
point in the rotated coordinate system. 𝛳 = 30𝑜 , (1,3)
Ans:
4. A big room is constructed so that the ceiling is a dome that is semielliptical in shape. If a
person stands at one focus and speaks, the sound that is made bounces off the ceiling
and gets reflected to the other focus. Thus, if two people stand at the foci (ignoring their
heights), they will be able to hear each other. If the room is 34 m long and 8 m high, how
far from the center should each of two people stand if they would like to whisper back
and forth and hear each other?

Ans:

5. The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate system.
The coordinates of a point in the xy-coordinate system are given. Find the coordinates of
the point in the rotated coordinate system. 𝛳 = 90𝑜 , (0,3)
Ans:

6. Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.
Sketch the graph of the resulting equation, showing both sets of axes.

b. xy – 2y – 4x = 0
ans:
7. Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.
5x2 – 6xy + 5y2 – 12 = 0
Ans:
8. A type of Conic where the plane intersects only on one cone to form an anbounded
curve.
Ans:
9. Rotate the axes to eliminate the xy-term in the equation.Then write the equation in
standard form. Sketch the graph of the resulting equation, showing both sets of axes.
a. x2 – 2xy + y2 – 1 = 0
Ans:
10. The x’y’-coordinate system has been rotated θ degrees from the xy-coordinate
system. The coordinates of a point in the xy-coordinate system are given. Find the
coordinates of the point in the rotated coordinate system.

a.Θ = 45o, (2, 1)


Ans:

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