The graph of 6x^{2}+5xy+3y^{2}-3x+5y=0 is
a

Calculate the discriminant.

With the graph of Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0,
find B^{2}-4AC (the discriminant)

In 6x^{2}+5xy+3y^{2}-3x+5y=0,
B=5, A=6 and
C=3

B^{2}-4AC=5^{2}-4(6)(3)=-47<0 (if
discriminant is more than
zero) – the graph is a ellipse.