Answer
(a) $F\lt17$
(b) $F=17$
(c) $F\gt17$
Work Step by Step
Form squares with the variables: $4(x^2+x+\frac{1}{4})+(y^2-8y+16)=1+16-F$ or $4(x+\frac{1}{2})^2+(y-4)^2=17-F$
(a) For the function to be an ellipse, we need $17-F\gt0$ or $F\lt17$
(b) For the function to be a single point, we need $17-F=0$ or $F=17$
(c) For the function to be the empty set, we need $17-F\lt0$ or $F\gt17$
