Given the length of the major and minor axis how to write the equation of the ellipse

The video tutorial explains how to write the equation of an ellipse given the lengths of the major and minor axes and the center at (0,0). It covers the setup of the equation, understanding the roles of the major and minor axes, and calculating distances from the center to the vertices and co-vertices. The tutorial concludes with the final equation setup.

What is the general form of the equation of an ellipse centered at (h, k)?

• (x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

• (x - h)^2 + (y - k)^2 = r^2

• (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

• (x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

If the major axis length is 8, what is the distance from the center to each vertex?

• 2

• 8

• 4

• 6

What does the variable 'a' represent in the context of an ellipse?

• The length of the major axis

• The length of the minor axis

• The distance from the center to a vertex

• The distance from the center to a co-vertex

If the minor axis length is 4, what is the distance from the center to each co-vertex?

• 1

• 2

• 4

• 3

What is the final equation of the ellipse given the major axis length of 8, minor axis length of 4, and center at (0,0)?

• x^2 / 16 + y^2 / 4 = 1

• x^2 / 4 + y^2 / 16 = 1

• x^2 / 8 + y^2 / 2 = 1

• x^2 / 2 + y^2 / 8 = 1