Questions in coordinate

Select	Question
	A point moves such that the sum of its distances from two fixed points (ae,0) and (–ae,0) is always 2a. Then equation of its locus is
	A point moves in such a way that its distance from (1,–2) is always the twice from (–3,5), the locus of the point is
	A point moves in such a way that its distance from origin is always 4. Then the locus of the point is
	If $A(-a,0)$ and $B(a,0)$are two fixed points, then the locus of the point on which the line AB subtends the right angle, is
	If A and B are two fixed points and P is a variable point such that $PA+PB=4$, then the locus of P is a/an
	If A and B are two points in a plane, so that $PA-PB$ = constant, then the locus of P is
	If A and B are two fixed points in a plane and P is another variable point such that $P{{A}^{2}}+P{{B}^{2}}=$constant, then the locus of the point P is
	The locus of P such that area of $\Delta PAB=12sq.$ units, where $A(2,3)$ and $B(-4,5)$ is
	The position of a moving point in the XY-plane at time t is given by $\left( (u\cos \alpha )t,(u\sin \alpha )t-\frac{1}{2}g{{t}^{2}} \right),$ where $u,\,\alpha ,\,g$are constants. The locus of the moving point is
	If $A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,-\cos \alpha ),\,C(1,\text{ }2)$are the vertices of a $\Delta ABC$, then as $\alpha $varies, the locus of its centroid is