Graphing Rotated Ellipses and Conics

Graphing Rotated Ellipses and Conics

Assessment

Interactive Video

Created by

Thomas White

Mathematics

9th - 10th Grade

Hard

The video tutorial explains how to graph a rotated conic section, specifically an ellipse. It begins by discussing the standard form of an ellipse and how to graph it without rotation. The tutorial then covers the process of rotating the ellipse by 30 degrees and converting the vertices to the XY plane using conversion equations. Finally, it demonstrates how to calculate the new vertex positions and finalize the graph of the rotated ellipse.

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13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main challenge in graphing a rotated conic section?

Finding the center of the ellipse

Identifying the type of conic section

Calculating the area of the ellipse

Dealing with the rotation of the axes

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the equation X'²/36 + Y'²/64 = 1 represent?

A circle

A hyperbola

An ellipse

A parabola

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How far do we go along the x-axis to plot the vertices of the ellipse without rotation?

10 units

4 units

6 units

8 units

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What additional term is included in the equation when the ellipse is rotated?

A Y² term

An X² term

An XY term

A constant term

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the angle of rotation applied to the ellipse in this example?

45 degrees

60 degrees

30 degrees

15 degrees

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the new axis called after rotation?

X-axis and Y-axis

X' axis and Y' axis

Z-axis and W-axis

A-axis and B-axis

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in converting the vertices from the rotated plane to the original plane?

Identifying the type of conic

Calculating the area

Finding the center

Using conversion equations

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