# Ellipses Shifts

Topic:
Ellipse

## Directions

1. Use the sliders to explore the parameters involved in determining the equation of the ellipse. 2. Answer the questions below.

## Question 1

What do "h" and "k" represent in the equation of an ellipse?

## Question 2

What happens to the ellipse when a<b? when a>b? when a=b?

## Question 3

What happens to the ellipse when a=b? What special kind of ellipse is this?

## Question 4

Let a=3 and b=3. The equation of the ellipse is shown for you. How can you rewrite the equation so that the equation is in the same form of another conic you have seen?

## Question 5

How are the values of the points V1, V2, V3, and V4 determined?

## Question 6

The vertices are defined as the points of the ellipse that are on the major axis, the longer diameter of the ellipse, while the covertices are the points of the ellipse that are on the minor axis, the shorter diameter of the ellipse. Determine when V1, V2, V3, and V4 will be vertices or co-vertices.

## Question 7

How do you find the distance between the foci and the center C? Give your answer in terms of a and b. (Hint: let a=5 and b=4. What is the distance between the foci and the center C here? What is the relationship between the two?)

## Question 8

How are the values of the foci determined? (Hint: use your answer in question 7 to help.) Give answers for when a<b and when a>b.

## Question 9

What is the equation of the ellipse in "Ellipse Equation #1"?

Check all that apply

## Question 10

Determine the equation of the ellipse in "Ellipse Equation #2."

## Question 11

What is the value of one of the foci of the equation: ?

Check all that apply