Post on 22-Dec-2015
Ellipses(page 7)
General form is
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
where A ≠ C and A and C are same sign
Standard form:
Major Axis:
Center:
‘a’:
‘b’:
Vertices:
Covertices:
2 2
2 21
x h y k
a b
The variable with the longest axis
,h k
Distance in the x direction
Distance in the y direction
Endpoints of the major axis
Endpoints of the minor axis
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.
1) Graph the ellipse
6
4
2
-2
-4
-6
-5 5
2 22 ( 1)1
9 36
y x
Length of major axis:
Length of minor axis:
Horizontal or vertical: