Diagram 4 shows an equilateral $\displaystyle ABCD$.Given that $\displaystyle C$ lies on the perpendicular bisector of $\displaystyle AD$ and the equation of $\displaystyle DC$ is $\displaystyle x=5y-17$

Find

(a) the equation of $\displaystyle AB$

(b)the coordinates of point $\displaystyle C$

(c)the equation of locus of a moving point such that its distance from point $\displaystyle A$ is twice distance from $\displaystyle D$