Understanding Ellipses

This video tutorial introduces the concept of an ellipse, explaining its definition and properties. It covers the standard form of an ellipse, how to identify its major and minor axes, and how to find the foci. The video also demonstrates how to graph an ellipse using these properties and provides example problems to reinforce the concepts. The tutorial aims to equip learners with the skills to graph ellipses and understand their geometric properties.

What is the constant sum of distances from any point on an ellipse to its two foci called?

• Radius

• Diameter

• Circumference

• Focal Constant

In the standard form of an ellipse, what do the variables h and k represent?

• The foci of the ellipse

• The coordinates of the center

• The eccentricity

• The lengths of the axes

How can you determine if the major axis of an ellipse is horizontal?

• The larger denominator is under the x part

• The larger denominator is under the y part

• The ellipse is a circle

• The foci are on the y-axis

What is the relationship between a, b, and c in an ellipse?

• b^2 = a^2 + c^2

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

• c^2 = a^2 + b^2

If an ellipse has a vertical major axis, how do you find the coordinates of the foci?

• Add and subtract c from the x-coordinate

• Add and subtract c from the y-coordinate

• Add and subtract a from the x-coordinate

• Add and subtract b from the y-coordinate

What is the length of the major axis if a = 3?

• 9

• 6

• 12

• 3

In the example with center (3, -1), what is the length of the minor axis?

• 8

• 2

• 4

• 6

For an ellipse with a horizontal major axis, what is the formula to find c?

• a^2 = b^2 + c^2

• b^2 = a^2 + c^2

• c^2 = a^2 + b^2

• a^2 + b^2 = c^2

What is the center of the ellipse if the equation is in the form (x + 2)^2/9 + (y - 1)^2/1 = 1?

• (2, 1)

• (-2, 1)

• (2, -1)

• (-2, -1)

How do you find the foci for an ellipse with a horizontal major axis?

• Add and subtract b from the x-coordinate

• Add and subtract a from the y-coordinate

• Add and subtract c from the x-coordinate

• Add and subtract c from the y-coordinate