1. Graph and Write Equations of Ellipses
Notes 9.4 (Day 1)
Graph and Write Equations of Ellipses

2. Vocab!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Ellipse: Like an oval
Foci:
Plural for focus
Sum of the distances from the foci to any point on the ellipse remains constant

3. More Vocab  Major Axis:
The axis that goes through the foci and center point
Minor Axis:
The axis that only goes through the center point

4. Even More VOCABULARY!! Vertices:
The points that are farthest from the origin on the major axis
Co-Vertices:
The points that are the farthest from the origin on the minor axis

5. Graphing Ellipses Ellipses:
h and k are both the opposite of what you think (just like a circle)
(h, k) is the center point of the ellipse.

6. Standard Equation of an Ellipse
Major axis:
Horizontal
Vertices:
Co-Vertices:
IMPORTANT!!! ***The a value is always the greater number.
Focus Points: OR

7. Standard Equation of an Ellipse
Major axis:
Vertices:
Co-Vertices:
Vertical
IMPORTANT!!! ***The a value is always the greater number.
Focus Points: OR

8. How to graph an ellipse:
Step 1: Determine whether a (the bigger number) is underneath x2 or y2.
Step 2: Find both the a and b values by square rooting the numbers under x2 and y2.
Step 3: Draw a coordinate plane.
Step 4: Place your center point at (h, k), this is your new “origin”
Step 4: Label the vertices (a) and co-vertices (b) (Depends on whether a is under x2 or y2)
Step 5: Find the foci. (c2 = a2 – b2, *don’t forget to square root*)
Step 6: Graph the foci.

9. Graph the equation. List the vertices, co-vertices, major axis, and focus points.

10. Graph the equation. List the vertices, co-vertices, major axis, and focus points.

11. Graph the equation. List the vertices, co-vertices, major axis, and focus points.

12. Graph the equation. List the vertices, co-vertices, major axis, and focus points.

13. Putting the Ellipse into Standard Form:
Step 1: Solve for the constant Step 2: Complete the square with both the x and y values Step 3: Divide both sides by the appropriate number to make the constant equal to 1

14. Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

15. Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

16. Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

17. Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

18. Homework:
Graphing and Properties of Ellipses