Practice!

Sample Problem

The graph of 6x2+5xy+3y2-3x+5y=0 is a

Solution

Calculate the discriminant.

With the graph of Ax2+Bxy+Cy2+Dx+Ey+F=0, find B2-4AC (the discriminant)

In 6x2+5xy+3y2-3x+5y=0, B=5, A=6 and C=3

B2-4AC=52-4(6)(3)=-47<0 (if discriminant is more than zero) – the graph is a ellipse.