# Section 10.4

```Ellipses
(page 7)
General form is
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
where A ≠ C and A and C are same sign
 x  h
Standard form:
Major Axis:
a
2
2
y k


b
2
2
The variable with the longest axis
Center:  h, k 
‘a’:
Distance in the x direction
‘b’:
Distance in the y direction
Vertices:
Covertices:
1
Endpoints of the major axis
Endpoints of the minor axis
Ex. Write the equation of the ellipse.
1) Find the center
2) Find a and b
3) Simplify
1) Write the equation of the ellipse.
2) Write the equation of the ellipse.
To graph, we may need to put the equation
into standard form.
 This may require us to complete the
square for the x terms and the y terms.
 Notice that standard form has
everything equal to 1.
2
y

2


( x  1)
1) Graph the ellipse

1
9
36
2
6
4
2
Length of major axis:
-5
5
Length of minor axis:
-2
Horizontal or vertical:
-4
-6
2) Graph the ellipse 16x2 + 32x = -y2
6
4
2
-5
5
-2
-4
-6
3) Graph the ellipse 4x2 + 9y2 – 16x + 54y + 61 = 0
6
4
2
-5
5
-2
-4
-6
```