$2$ Geometric meaning of second order condition $-$ Example $1$

Consider the following constrained maximization problem.

maxf$(x,y)s.t.ax+by=c$

For simplicity, assume $a>0,b>0,c>0.$ Also assume $f_x>0$ and $f_y>0.$

$($a$)$ State the second order condition for this constrained maximization problem.

$($b$)$ Find the condition for $\frac{d}{dx}(\frac{f_x}{f_y})>0$ subject to $f(x,y)=$ for given $inR.$

$($c$)$ Compare the answer for parts $($a$)$ and $($b$),$ and provide a geometric interpretation.