Understanding Ellipses

The video tutorial explains how to determine the properties of an ellipse, including its center, vertices, and foci. It covers the standard equations for ellipses with horizontal and vertical major axes, and how to identify these axes based on the equation's denominators. The tutorial also demonstrates how to calculate the foci using the equation c^2 = a^2 - b^2 and provides steps to plot the ellipse on a coordinate plane.

What are the two forms of the standard equation of an ellipse based on?

• The color of the ellipse

• The size of the ellipse

• The number of vertices

• The orientation of the major axis

If the larger denominator is under the X part of the equation, what type of major axis does the ellipse have?

• Vertical

• Circular

• Horizontal

• Diagonal

What is the center of the ellipse given the equation (x-4)^2/25 + (y+2)^2/4 = 1?

• (5, 2)

• (0, 0)

• (4, -2)

• (-4, 2)

How do you find the endpoints of the major axis?

• Add and subtract 'a' from the x-coordinate

• Add and subtract 'b' from the x-coordinate

• Add and subtract 'b' from the y-coordinate

• Add and subtract 'a' from the y-coordinate

What is the length of the major axis?

• b units

• 2b units

• a units

• 2a units

What is the formula used to find the foci of the ellipse?

• c^2 = b^2 - a^2

• c^2 = a^2 * b^2

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

Where are the foci located in relation to the major axis?

• On the minor axis

• On the major axis

• Outside the ellipse

• At the center

What is the approximate y-coordinate of the first focus?

• 4.58

• 3.58

• 2.58

• 5.58

What is the approximate y-coordinate of the second focus?

• 9.58

• 8.58

• 7.58

• 6.58

What is the final step in sketching the ellipse?

• Sketching the ellipse through the vertices

• Drawing the major axis

• Plotting the center

• Calculating the foci