Ellipse

Intro to Ellipses

Self-Paced Lesson (Part 1)

Poll

How Are You Today?

• Awesome

• "I'm in math class, so...yeah"

• Okay

What's a Foci? - COPY DOWN!!

• Foci is the plural of Focus

• You'll remember that Parabolas had just one Focus

• Since Ellipses have two of them, they are called Foci, or F1 and F2 symbolically

Multiple Choice

What is the Term that we used for the plural of Focus?

• Focuses

• Foci

• Fungi

• Ford

Multiple Choice

How many Foci are there in an Ellipse

• 0

• 1

• 2

• 3

Equations of Ellipses - COPY DOWN!!!!

• a² is always assigned to the largest denominator

• If the larger denominator is under the x, it is a Horizontal ellipse

• If the larger denominator is under the y, it is a Vertical ellipse

• Note that the Center of the Ellipse still uses the same (h,k) as the Circle did

Multiple Choice

If the Larger Denominator is under the y, then the Ellipse will be:

• Vertically Positioned

• Horizontally Positioned

Multiple Choice

The a² is always assigned to the:

• Larger Denominator

• Smaller Denominator

What are the a and b used for? - COPY DOWN!

• Other than telling us if the graph is Horizontal or Vertical:

• 'a' values are used to find the Vertices points

• 'b' values are used to find the Co-Vertices points

What are Vertices and Co-Vertices? COPY DOWN!!!

• Vertices are the two points on the Ellipse that are FARTHEST from the Center

• Co-Vertices are the two points on the Ellipse that are CLOSEST to the Center

Multiple Choice

Vertices points are _______ from the Center, while Co-Vertices points are _______ from/to the Center

• Closest, Farthest

• Farthest, Closest

Horizontal Major Axis - COPY DOWN!

• Vertices Coordinates:

• (h - a, k) and (h + a, k)

• Co-Vertices Coordinates:

• (h, k - b) and (h, k + b)

Example: COPY DOWN!!!

• Center is at (-2, -2) Remember, h and k are opposite from the equation

• a² would be assigned to the 9, which means a = 3

• By default, that means that b² would be assigned to the 4, which would lead to b = 2

• This would be a Horizontal Major Axis Ellipse, because the a² is under the x

Multiple Choice

Using the Formulas for the Vertices, what would be the correct Vertices for this example from the previous slide?

• (-3, -2) and (1, -2)

• (-5, -5) and (0, -3)

• (3, 2) and (5, 2)

• (-5, -2) and (1, -2)

Multiple Choice

Using the same example, using our formulas for the Co-Vertices, what are the correct coordinates for the Co-Vertices?

• (-2, 0) and (-2, -4)

• (-2, -2) nd (-2, 3)

• (-5, -2) and (1, -2)