Locus and Its Equation

A point is such that its distance from the point$(3,0)$ is twice its distance from the point $(-3,0)$ Find the equation of the locus. 

Find the locus of the point $P(x,y)$ such that the area of the triangle $PAB\text{ is }5$, where $A$ is the point $(1,-1)$ and $B$ is the point $(5,2)$.

A point $P (x, y)$ is such that its distance from the fixed point $(\alpha ,0)$ is equal to its distance from $y-$axis. Prove that the equation of the locus is $y^2=\alpha (2x-\alpha )$.