Writing and Graphing Ellipses in Standard Form

This video tutorial focuses on ellipses, covering how to graph them, find the coordinates of vertices and foci, and write equations in standard form. It explains the differences between ellipses with horizontal and vertical major axes, and how to adjust equations for ellipses not centered at the origin. The tutorial includes practice problems to reinforce the concepts.

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

• 2b

• a

• 2a

• b

For an ellipse centered at the origin, what is the equation for a horizontal ellipse?

• x^2 - y^2 = 1

• x^2/b^2 + y^2/a^2 = 1

• x^2/a^2 + y^2/b^2 = 1

• x^2 + y^2 = 1

How do you determine if an ellipse is elongated in the x or y direction?

• By comparing the values of x and y

• By comparing the values of h and k

• By comparing the values of c and d

• By comparing the values of a and b

What are the coordinates of the foci for an ellipse with a horizontal major axis centered at the origin?

• 0, ±c

• ±c, 0

• ±a, 0

• 0, ±a

What is the equation for an ellipse not centered at the origin?

• x^2 + y^2 = 1

• (x - h)^2/a^2 + (y - k)^2/b^2 = 1

• x^2/a^2 + y^2/b^2 = 1

• (x + h)^2/a^2 + (y + k)^2/b^2 = 1

How do you find the new coordinates of the foci for an ellipse not centered at the origin?

• Add h to x and k to y

• Add ±c to h and k

• Add ±b to h and k

• Add ±a to h and k

What is the formula to calculate c for an ellipse?

• c = a - b

• c = a + b

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

If a^2 is 16 and b^2 is 9, what is the value of c?

• √9

• √5

• √25

• √7

For an ellipse centered at (3, -2) with a^2 = 25 and b^2 = 16, what is the equation in standard form?

• (x - 3)^2/25 + (y + 2)^2/16 = 1

• (x - 3)^2/16 + (y + 2)^2/25 = 1

• (x + 3)^2/25 + (y - 2)^2/16 = 1

• (x + 3)^2/16 + (y - 2)^2/25 = 1

What are the coordinates of the center for the ellipse given by the equation (x - 1)^2/9 + (y + 1)^2/4 = 1?

• (-1, 1)

• (1, -1)

• (1, 1)

• (-1, -1)