Chapter 11.3, Problem 90AYU

(a)

To determine

Show that the equation $A{x}^2+C{y}^2+Dx+Ey+F=0$ is the equation of an ellipse $\frac{D^2}{4A}+\frac{E^2}{4C}-F$ is same sign as A.

(b)

To determine

Show that the equation $A{x}^2+C{y}^2+Dx+Ey+F=0$ is a point if $\frac{D^2}{4A}+\frac{E^2}{4C}-F=0$.

(c)

To determine

Show that the equation $A{x}^2+C{y}^2+Dx+Ey+F=0$ has contain no point if $\frac{D^2}{4A}+\frac{E^2}{4C}-F$ is opposite sign of A.