Lesson Graphing of ellipses

Source code of 'Graphing of ellipses'

This Lesson (Graphing of ellipses) was created by by Alwayscheerful(414)

: View Source, Show
About Alwayscheerful: I'm available as an online paid tutor if anyone need extensive 1 on 1 help. =)

Ellipses are actually very special cases of circles.  
All we need to get started is the standard form of an ellipse and that is:
{{{((x-h)^2)/a^2+((y-k)^2)/b^2=1}}}
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
{{{((x+2)^2)/9+((y-4)^2)/25=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.

{{{ drawing( 400, 400, -10, 10, -10, 10, grid( 1 ), red( ellipse( -2, 4, 3, 5 ) ) ) }}}

EXAMPLE 2
{{{(x^2)/49+((y-3)^2)/4=1}}}
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.

{{{ drawing( 400, 400, -10, 10, -10, 10, grid( 1 ), red( ellipse( 0, 3, 7, 2 ) ) ) }}}

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.
{{{((x-h)^2)/a^2+((y-k)^2)/a^2=1}}}
Now since they are equal, we can get rid of the denominators.
{{{(x-h)^2+(y-k)^2=1}}}
Seem familiar?
**If not, the standard form of a circle is {{{(x-h)^2+(y-k)^2=r^2}}}**  :)
Hope this helps!