Understanding Ellipses

The video tutorial explains how to identify the center and radii of an ellipse given its equation. It starts by introducing the equation and choices, then details how to find the center by examining the equation's structure. The tutorial verifies the center and calculates the horizontal and vertical radii, confirming the equation's correctness.

What is the general form of an ellipse equation?

• x^2 + y^2 = 1

• (x-h)^2/a^2 + (y-k)^2/b^2 = 1

• x^2 - y^2 = 1

• (x-h)^2 - (y-k)^2 = 1

How can you determine the center of an ellipse from its equation?

• By finding the intercepts on the axes

• By calculating the area of the ellipse

• By identifying the values of h and k in the equation

• By looking at the coefficients of x and y

What is the center of the ellipse given by the equation x minus 4 squared over 16 plus y minus 1 squared over 49 equals 1?

• (4, 1)

• (0, 0)

• (16, 49)

• (1, 4)

Which choice has the correct center for the given ellipse equation?

• The one with center (0, 0)

• The one with center (4, 1)

• The one with center (1, 4)

• The one with center (16, 49)

What is the length of the horizontal radius of the ellipse?

• 4

• 7

• 16

• 49

What is the length of the vertical radius of the ellipse?

• 4

• 7

• 16

• 49

How do you verify the horizontal radius from the equation?

• By checking if it matches the coefficient of x

• By ensuring it is the square root of the denominator under x

• By calculating the area of the ellipse

• By comparing it to the vertical radius

How do you verify the vertical radius from the equation?

• By calculating the circumference of the ellipse

• By comparing it to the horizontal radius

• By ensuring it is the square root of the denominator under y

• By checking if it matches the coefficient of y