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

Ex. Write the equation of the ellipse.1) Find the center2) Find a and b3) 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.

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:

2) Graph the ellipse 16x2 + 32x = -y2

6

4

2

-2

-4

-6

-5 5

3) Graph the ellipse 4x2 + 9y2 – 16x + 54y + 61 = 0

6

4

2

-2

-4

-6

-5 5