Problem #$5$: Find the points on the graph of $f(x,y)=(y+9)(x-8{)}^5$ at which the tangent plane is horizontal.

$($A$)$ All points on the line $r(t)=($:$0,t,0$:$)$

$($B$)$ All points on the line $r(t)=($:$-9,t,0$:$)$

$($C$)$ All points on the line $r(t)=($:$t,0,0$:$)$

$($D$)$ The point $(8,-9,0)$ only

$($E$)$ All points on the line $r(t)=($:$t,-9,0$:$)$

$($F$)$ All points on the line $r(t)=($:$8,t,0$:$)$

$($G$)$ All points on the line $r(t)=($:$t,8,0$:$)$

$($H$)$ The point $(-9,8,0)$ only