Question

Except for degenerate cases, the equation$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$defines an ellipse if ________ .

Short answer

Except for degenerate cases, the equation$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$defines an ellipse if$\underline{B^2-4AC<0}$.

Step-by-step solution

Step 1. Given information

An equation is$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$

Step 2. Fill in the blank.

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

If$B^2-4AC<0$, an equation defines an ellipse if$B^2-4AC<0$