$($D points$)$ Find all points at which the direction of greatest rate of change of the function $f(x,y)=x^2+y^2-2x-4y$ is vec$(i)+$vec$(j).$

a$)y=x-1$

b$)y=-x+1$

c$)y=-x-1$

d$)y=x+1$

e$)y=2x$