Understanding Ellipses

The video tutorial explains how to derive the equation of an ellipse given specific conditions. It starts by identifying the foci and the center of the ellipse, then moves on to plotting these points. The tutorial explains the relationship between the sum of distances from any point on the ellipse to the foci and the major axis. It derives the equation of the ellipse by calculating the values of A and B, using the formula A^2 = B^2 + C^2, and concludes with the final equation.

What is the shape of the graph described in the problem?

• Ellipse

• Circle

• Parabola

• Hyperbola

Where is the center of the ellipse located?

• At (5, 0)

• At (-5, 0)

• At the origin

• At (0, 5)

What is the value of C, the distance from the center to a focus?

• 3

• 4

• 5

• 6

What is the length of the major axis of the ellipse?

• 10

• 12

• 14

• 16

What is the value of A, half the length of the major axis?

• 6

• 7

• 5

• 4

Why does the sum of distances from any point on the ellipse to the foci equal 2A?

• Because of the definition of a hyperbola

• Because of the definition of a parabola

• Because of the definition of an ellipse

• Because of the definition of a circle

What formula is used to find B in the ellipse equation?

• A squared equals B squared plus C squared

• A squared equals B squared times C squared

• A squared equals B squared minus C squared

• A squared equals C squared minus B squared

What is the value of B squared in the ellipse equation?

• 9

• 10

• 11

• 12

What is the equation of the ellipse derived in the video?

• X squared/11 + Y squared/36 = 1

• X squared/36 + Y squared/11 = 1

• X squared/25 + Y squared/11 = 1

• X squared/36 + Y squared/25 = 1

What is the significance of the larger denominator in the ellipse equation?

• It is always under the X part

• It is always under the Y part

• It indicates the minor axis

• It indicates the major axis