Questions in coordinate

Select	Question
	If the equation of the locus of a point equidistant from the points $({{a}_{1}},{{b}_{1}})$ and $({{a}_{2}},{{b}_{2}})$ is $({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})y+c=0$, then the value of c is
	If sum of distances of a point from the origin and lines $x=2$ is 4, then its locus is
	The locus of a point whose difference of distance from points (3, 0) and (–3,0) is 4, is
	Locus of centroid of the triangle whose vertices are $(a\cos t,a\sin t),\ (b\sin t,-b\cos t)$ and (1, 0), where t is a parameter; is
	If the distance of any point P from the point $A(a+b,a-b)$ and $B(a-b,a+b)$are equal, then the locus of P is
	What is the equation of the locus of a point which moves such that 4 times its distance from the x-axis is the square of its distance from the origin
	Let P be the point (1, 0) and Q a point of the locus ${{y}^{2}}=8x$. The locus of mid point of PQ is