# Identify the type of graph

• Mar 4th 2012, 11:35 AM
SammyAbby
Identify the type of graph
How do I graph this equation on a ti-83? I am struggling with this particular type of problem...I would like to learn how to do this on my calculator so that I will always know for future reference...any help is greatly appreciated!
Attachment 23308
• Mar 4th 2012, 01:48 PM
skeeter
Re: Identify the type of graph
Quote:

Originally Posted by SammyAbby
How do I graph this equation on a ti-83? I am struggling with this particular type of problem...I would like to learn how to do this on my calculator so that I will always know for future reference...any help is greatly appreciated!
Attachment 23308

complete the square for both x and y ...

$\displaystyle 6x^2 - 12x + 7y^2 + 42y = 57$

$\displaystyle 6(x^2 - 2x) + 7(y^2 + 6y) = 57$

$\displaystyle 6(x^2 - 2x + 1) + 7(y^2 + 6y+9) = 57 + 6 + 63$

$\displaystyle 6(x-1)^2 + 7(y+3)^2 = 126$

$\displaystyle \frac{(x-1)^2}{21} + \frac{(y+3)^2}{18} = 1$

you should recognize the above general form equation for an ellipse.

if you wish to graph it in your calculator, you'll have to solve for y, getting equations for the upper and lower branches of the ellipse and graphing those in Y1 and Y2.
• Mar 4th 2012, 02:27 PM
SammyAbby
Re: Identify the type of graph
Thank you for your assistance...if you do not mind me asking...how did you get the 21 and 18 as the denominators?
• Mar 4th 2012, 05:12 PM
skeeter
Re: Identify the type of graph
Quote:

Originally Posted by SammyAbby
Thank you for your assistance...if you do not mind me asking...how did you get the 21 and 18 as the denominators?

6/126 = 1/21

7/126 = 1/18