Lesson Graphing of ellipses

Ellipses are actually very special cases of circles.
All we need to get started is the standard form of an ellipse and that is:

REMEMBER: The right side of the equation must be 1 in order to be in standard form.
The point (h,k) is most commonly referred to as the CENTER.
In order to graph an ellipse, you need 4 points:
Right point (h+a,k)
Left point (h-a,k)
Top point (h,k+b)
Bottom point (h,k-b).

Note that a is the square root of the number under the x term and is the amount that we move right and left from the center.
B is also the square root of the number under the y term and is the amount that we move up or down from the center.

EXAMPLE 1

The center of the ellipse will be (-2,4) **CAREFUL WITH SIGNS**
a=3, b=5
We can then derive the rest of the points
Right point - (h+a,k)=(1,4)
Left point - (h-a,k)=(-5,4)
Top point - (h,k+b)=(-2,9)
Bottom point - (h,k-b)=(-2,-1)
Then connect the points with smooth lines, making an oval.

EXAMPLE 2

Center: (0,3)
a=7, b=2
Right point - (7,3)
Left point - (-7,3)
Top point - (0,5)
Bottom point - (0,1)
Then connect the points with smooth lines, making an oval.

Now why are ellipses a special case of cirlces?
First, let's assume a=b. In that case, we would end up with the following formula.

Now since they are equal, we can get rid of the denominators.

Seem familiar?
**If not, the standard form of a circle is ** :)
Hope this helps!