1. 10.4, Day 2 More Ellipses!!

2. Do Now  Consider an elliptical fountain that is 10 feet long (x) and 20 feet wide (y). Write an equation to model the fountain. What is the area of the fountain?  Check your homework answers.

3. Homework Answers Q1: -Major axis: 40 feet -Minor axis: 30 feet Q2: Q3: Endpoints of major axis: (20,0) and (-20,0) Endpoints of minor axis: (0,15) and (0,-15) Foci (rounded to nearest tenth): (13.2,0) and (-13.2,0) Q4: ft 2 (about 942.48 ft 2)

4. Back of the Sheet a. Center (0,0); Vertices (0,13) and (0,-13); Co-vertices (12,0) and (-12,0); Foci (0,5) and (0,-5); Length of major axis 26; Length of minor axis 24 b. Center (0,0); Vertices (2,0) and (-2,0); Co-vertices (0, sqrt(2)) and (0,-sqrt(2)); Foci (sqrt(2),0) and (-sqrt(2),0); Length of major axis 4; Length of minor axis 2*sqrt(2) c. A bit messy! If you got this one, you’re a champ. Center (1,-1); Vertices (9/4,-1) and (-1/4,-1); Co- vertices (1,0) and (1,-2); Foci (7/4, -1) and (1/4,-1); Length of major axis 5/2; Length of minor axis 2

5. More d. e.

7. Standard Form Write in standard form. Is it a circle or is it an ellipse? If it is a circle, identify the center and radius. If it is an ellipse, identify the center, vertices, co-vertices, and foci. For the circle, write its equation in elliptical form. A) x 2 +9y 2 -4x+54y+49=0 B) 3x 2 +18x+12y+3y 2 =36

8. One More Example as a Class Write the equation of an ellipse if the endpoints of the major axis are at (-11,5) and (7,5) and the endpoints of the minor axis are at (-2,9) and (-2,1).

9. Ellipses Graph (identify vertices, co-vertices, major axis, minor axis, foci) Write equations of ellipses in standard form Write equations of circles in elliptical form Area of an ellipse Writing equations of ellipses given various pieces of information Determine if something is a circle or an ellipse

10. Practice Problems for Quiz Work with your 12:00 partner on the quiz review problems.