Graphing an ellipse and converting to a standard form

[Louise Johnson]

3x²-12x+y²+3=0


To graph this problem I just isolated Y to one side so that I could graph it using my calculator and came up with :
y=+or- the Sqrt -3x²+12+3


My big problem was trying to convert the general form of the equation to a standard form which usually involves completing the square. Immediately I can see that this will be an ellispe when it is graphed because the sign of the squares are the same and the numerical coefficients are different.

Any help would be appreciated
Thanks
Louise

 

[skeeter]

\(\displaystyle \L 3x^2 - 12x + y^2 + 3 = 0\)

\(\displaystyle \L 3(x^2 - 4x) + y^2 = -3\)

\(\displaystyle \L 3(x^2 - 4x + 4) + y^2 = -3 + 12\)

\(\displaystyle \L 3(x - 2)^2 + y^2 = 9\)

\(\displaystyle \L \frac{(x-2)^2}{3} + \frac{(y-0)^2}{9} = 1\)

 

[Louise Johnson]

Thank you agian Skeeter. It's clearly my inability to complete the square easily. I am going to spend more time on it and this particular problem for that matter. Hopefully my isolating y on one side is ok. I will graph them both and find out.
Thank you !!!
Louise