The document discusses ellipses and provides examples of writing equations of ellipses in standard form given information about the center, vertices, co-vertices, major and minor axes, or dimensions. It includes examples of writing equations of translated ellipses, converting equations to standard form, and adding foci. The last sentences mention there will be a quiz the next day covering circles and ellipses.

1. Warm-Up
 Range Graphically
(#9 on CQ#1)

2. Homework Questions

3. Chapter 8
Ellipses

4. Ellipses
 Standard Form of an Ellipse
 Center (h, k)
 a is your hm (horizontal movement)
 b is your vm (vertical movement)
1
)()(
2
2
2
2
=
−
+
−
b
ky
a
hx

5. Graph
(and state vertices and co-vertices…major and minor axis)
1
8149
22
=+
yx

6. Graph
1
2536
22
=+
yx

7. Graph
1
9
)2(
64
)3( 22
=
+
+
− yx

8. Graph
164 22
=+ yx
225925 22
=+ yx

9. Write an equation of an
ellipse.
1. Center at the origin and vertex at (0,5) and
co-vertex at (2,0)
2. Center at the origin and vertex at (0,-6) and
co-vertex at (3,0)
3. Find an equation of an ellipse centered at
the origin that is 12 units wide and 30 units
high.

10. Additional Examples:
1. Write an equation in standard form of
an ellipse that has a vertex at (0,-4), a
co-vertex at (3,0) and is centered at
the origin.
2. Find an equations of an ellipse
centered at the origin that is 20 units
wide and 10 units high.

11. Write the equation of a
translated Ellipse
1. Write an equation of an ellipse with
center (-3,-2), vertical major axis of
length 8 and minor axis of length 6.
2. Write an equation of an ellipse with
center (1,-4), horizontal major axis of
length 10, and minor axis of length 4.

12. Write in Standard Form:
1. 25x²+16y²+150x = 160y-225
2. 2x²+8x+y²+4 = 0

13. Now you try…Write in
standard form.
1. 4x²+y² - 24x + 6y + 9 = 0
1. x² + y² - 12x+ 4y = 8

14. Add in Focus!!

15. Let’s look at #3 on your
worksheet…or others with foci

16. Homework
Worksheet
Quiz tomorrow on Circles and Ellipses!