



 
Donna, There are both x^{2} and y^{2} terms so it's not a parabola. The fact that the coefficients of the x^{2} and y^{2} terms are both positive means it's not a hyperbola. Since the coefficients of both the x^{2} and y^{2} terms are the same (they are both 3) it's probably a circle. All that remains is to put it in standard form
to check that the right side is positive. If the right side is zero then the radius of the circle is zero and the conic is just a point. If the right side is negative then there are no points on the graph of 3x² + 3y²  4y  8 = 0. To put the equation in standard form first divide through by 3 to get
Now complete the square of the expression y²  4/3 y  8/3 = 0. This will allow you to write
in the form
If the right side is positive then you have a circle. I hope this helps,  


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