Questions in coordinate

Select	Question
	O is the origin and A is the point (3,4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is
	The locus of a point which moves so that it is always equidistant from the point A(a, 0) and B (– a, 0) is
	The coordinates of the points A and B are (a, 0) and $(-a,\,0)$ respectively. If a point P moves so that $P{{A}^{2}}-P{{B}^{2}}=2{{k}^{2}}$, when k is constant, then the equation to the locus of the point P , is
	If the coordinates of a point be given by the equations $x=b\sec \varphi ,\ \ y=a\tan \varphi $, then its locus is
	The coordinates of the point A and B are $(ak,0)$ and $\left( \frac{a}{k},0 \right),\,\,(k=\pm 1)$. If a point P moves so that $PA=kPB,$ then the equation to the locus of P is
	The locus of a point which moves in such a way that its distance from (0,0) is three times its distance from the x-axis, as given by
	The equation of the locus of all points equidistant from the point (4,2) and the x-axis, is
	The locus of the mid-point of the distance between the axes of the variable line $x\cos \alpha +y\sin \alpha =p,$ where p is constant, is
	The locus of a point whose distance from the point $(-g,-f)$is always 'a', will be, (where $k={{g}^{2}}+{{f}^{2}}-{{a}^{2}}$)
	The locus of the moving point P, such that 2PA = 3PB where A is (0,0) and B is (4,–3), is