The coordinates of $\displaystyle E,F$ and $\displaystyle H$ of an equilateral are $\displaystyle (3,3),(0,-1)$and $\displaystyle (6,2)$ respectively.$\displaystyle FH$ is perpendicular to $\displaystyle EG$ whereas the straight line $\displaystyle FG$ is parallel to $\displaystyle x-axis$.Find

a)the equation of straight line $\displaystyle EG$

b)the coordinates of point $\displaystyle G$

c)the equation of locus $\displaystyle R$ such that the distance of $\displaystyle R$ from point $\displaystyle E$ and $\displaystyle F$ are equal.