Ellipse Properties and Equations

The video tutorial explains how to derive the equation of an ellipse given the lengths of its semi-major and semi-minor axes, and the equations of its major and minor axes. It starts by calculating the lengths of the axes, then finds the center of the ellipse by solving the axis equations. Using these parameters, the equation of the ellipse is formulated and simplified to its standard form.

What are the given lengths of the semi-major and semi-minor axes of the ellipse?

• √2 and 3

• 3 and √2

• √3 and 2

• 2 and √3

Which equation represents the major axis of the ellipse?

• x - 3 = 0

• y + 5 = 0

• y - 5 = 0

• x + 3 = 0

What is the center of the ellipse?

• (3, -5)

• (-3, 5)

• (5, -3)

• (-5, 3)

How is the standard form of the ellipse equation expressed?

• (x + h)^2/b^2 + (y + k)^2/a^2 = 1

• (x - h)^2/b^2 + (y - k)^2/a^2 = 1

• (x - h)^2/a^2 + (y - k)^2/b^2 = 1

• (x + h)^2/a^2 + (y + k)^2/b^2 = 1

What is the value of a^2 in the ellipse equation?

• 4

• 2

• 3

• √3

What is the value of b^2 in the ellipse equation?

• 3

• 4

• √3

• 2

What is the simplified form of the ellipse equation?

• 3(x + 3)^2 + 4(y - 5)^2 = 12

• 3(x - 3)^2 + 4(y + 5)^2 = 12

• 4(x + 3)^2 + 3(y - 5)^2 = 12

• 4(x - 3)^2 + 3(y + 5)^2 = 12

What is the coefficient of x^2 in the final equation of the ellipse?

• 40

• 18

• 3

• 4

What is the coefficient of y^2 in the final equation of the ellipse?

• 3

• 4

• 40

• 18

What is the constant term in the final equation of the ellipse?

• 115

• 12

• 27

• 100