The locus of the vertex $A$ of a triangle $ABC$,where the base $BC$ is fixed and the perimeter of the triangle is constant,is

The equation $\sqrt{(x - 2)^2 + y^2} + \sqrt{(x + 2)^2 + y^2} = 4$ represents a

The locus of the midpoint of the chords of the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ which makes an angle of $120^\circ$ at the centre is

The locus of the centers of the circles,which have the same area and have $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as their common tangents,is

If the locus of the point,whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$,is $ax^2+by^2+cxy+dx+ey+170=0$,then the value of $a^2+2b+3c+4d+e$ is equal to:

If $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$ are three given points,then the locus of a point $S$ satisfying the relation $SQ^2 + SR^2 = 2SP^2$ is