1. March 22 nd copyright2009merrydavidson

2. Horizontal Ellipse An ellipse is the set of all points for which the sum of the distances at 2 fixed points is a constant. (h,k) a c Vertex Co-Vertex

3. Horizontal Ellipse where a > b > 0 AND: c 2 = a 2 - b 2 “a 2 ” is under the “x” for horizontal.

4. The FOCUS is on the major axis. a = center to vertex b = center to co-vertex c = center to focus Length of major axis is 2a Length of minor axis is 2b IMPORTANT INFO…..

5. Ex 1: What is the center? (0,0) What is “a”? Go 5 right & left What is “b”? Go 3 up & down Find “c”. c 2 = a 2 - b 2 c 2 = 5 2 - 3 2 c 2 = 16 c = 4 (+4,0)

6. Vertical Ellipse (h,k) b Co-Vertex Vertex

7. VERTICAL ELLIPSE where a > b > 0 AND: c 2 = a 2 - b 2 The “a 2 ” is under the “y” for vertical.

8. Ex 2: What is the center? (3,-4) What is “a”? Go 6 up & down What is “b”? Go 4.5 right & left Find “c”. c 2 = a 2 - b 2 c 2 = 6 2 - 20 c 2 = 16 c = 4 (3,0),(3,-8)

9. Ex 3:Graph: 4y 2 + 16x 2 = 144 Divide by 144 so that it =‘s 1. What is “b”? Graph all of this. Find “c”. c 2 = a 2 - b 2 c = 16 Which direction is this? What is “a”? vertical (0,+4)

10. Ex 4: Complete the square x 2 + 4y 2 + 4x – 24y + 24 = 0

11. Ex 5: Write the equation for Endpoints of major axis @ (0,10) & (0,-10). Foci @ (0,8) & (0,-8) Graph what you know. Where is the center? Fill in what you can in the equation. Horizontal or Vertical?

12. Ex 5: Write the equation for c 2 = a 2 - b 2 8 2 = 10 2 - b 2 64 = 100 - b 2 b 2 = 36

13. Circles (x – h) 2 + (y – k) 2 = r 2 (h,k) r The set of all points that are equidistant from the center point.

14. When graphing you MUST label… center radius

15. Center: Radius: Ex 6: (4,- 1)

16. Center: Radius: Ex 7: (0,0) approximately 4.5

17. Divide by 4 first Center: Radius: Ex 8: (0,0)

18. Ex 9: complete the square Rearrange the order first. Group by 2’s & blanks. Fill in the blanks.

19. Ex 10: complete the square Rearrange the order first. Group by 2’s & blanks. Fill in the blanks.

20. Ex 10: continued What is the radius? What is the center? (9, -9)

21. Ex 11: Find the equation of the circle with center at (-1,5) and radius of 2. (x – h) 2 + (y – k) 2 = r 2

22. Ex 12: Find the equation of the circle with center at (-8,7) and radius of. (x – h) 2 + (y – k) 2 = r 2

23. Ex 13: Find the equation of the circle with center at (-1,4) and goes through the point (1, 0). (x – h) 2 + (y – k) 2 = r 2 (x,y)(h,k)

24. Ex 14: Find the equation of the circle with endpoints of the diameter at (-6,2) and (4,2) (x – h) 2 + (y – k) 2 = r 2

25. Worksheet for HW