I have to factor this to find what this graph looks like but I don't know if I'm doing it right.
6x^2-12x+6y^2+36y=36
3x^2-6x+3y^2+18y=18
I'm stopping there because I don't know if I divide by 2 or 6
In the original equation, all coefficents are multiples of six. Divide by six.
6x^2-12x+6y^2+36y=36
x^2-2x+y^2+6y=6
(x^2-2x+1)+(y^2+ I'm stuck
To determine the graph of the equation, it is important to simplify it and put it in the standard form for a conic section. In this case, the given equation is a conic section of the form Ax^2 + By^2 + Cx + Dy + E = 0.
Let's work on the first equation: 6x^2 - 12x + 6y^2 + 36y = 36. To factor it correctly, let's begin by grouping the x terms together and the y terms together:
(6x^2 - 12x) + (6y^2 + 36y) = 36
Now, we can factor out the common factor from each group:
6x(x - 2) + 6y(y + 6) = 36
At this point, we can divide every term by 6 to simplify the equation, which will not change the graph:
x(x - 2) + y(y + 6) = 6
So, the equation of the graph is x(x - 2) + y(y + 6) = 6.
Now, let's move to the second equation: 3x^2 - 6x + 3y^2 + 18y = 18. Following the same steps as before:
(3x^2 - 6x) + (3y^2 + 18y) = 18
Factoring out the common factor from each group:
3x(x - 2) + 3y(y + 6) = 18
Dividing every term by 3 to simplify:
x(x - 2) + y(y + 6) = 6
Notice that this equation is identical to the one we obtained in the first equation. Therefore, both equations represent the same graph.
To answer your question about dividing by 2 or 6, in this case, you can divide every term by either 2 or 6, but it is not necessary to do so. Dividing by a common factor is a way to simplify the equation, but it won't affect the shape or position of the graph.