Chapter 7.3, Problem 87AE

To determine

To find: Graph of an equation of the form $A{x}^2+C{y}^2 +Dx+Ey+F=0, A\ne 0,C\ne 0$ where $A$ and $C$ are of the same sign,

a. Is an ellipse if $\frac{D^2}{4A}+\frac{E^2}{4C}-F$ is the same sign as $A$.

b. Is a point $\frac{D^2}{4A}+\frac{E^2}{4C}-F=0$.

c. Contains no points if $\frac{D^2}{4A}+\frac{E^2}{4C}-F$ is of opposite sign to $A$.