Chapter 12.4, Problem 63E

To determine

(a)

The value of $F$ for which the graph of the equation $4x^2+y^2+4\left(x-2y\right)+F=0$ is an ellipse.

To determine

(b)

The value of $F$ for which the graph of the equation $4x^2+y^2+4\left(x-2y\right)+F=0$ is a single point.

To determine

(c)

The value of $F$ has to be greater than $17$ for the given equation $4x^2+y^2+4\left(x-2y\right)+f=0$ to represents an empty set.