# Thread: Identify the type of graph

1. ## 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!

2. ## Re: Identify the type of graph

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!
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.

3. ## 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?

4. ## Re: Identify the type of graph

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