If the equation of a curve remains unchanged by replacing $x$ and $y$ with $-x$ and $-y$ respectively,then the curve is

From a point $P$ on the circle $x^2+y^2=4$,two tangents are drawn to the circle $x^2+y^2-6x-6y+14=0$. If $A$ and $B$ are the points of contact of those lines,then the locus of the centre of the circle passing through the points $P, A$ and $B$ is

The locus of the moving point $P$,such that $2PA = 3PB$ where $A$ is $(0,0)$ and $B$ is $(4,-3)$,is

The locus of the midpoints of the chords of the circle $x^2-2x+y^2=0$ drawn from the point $(0,0)$ on it is

If the endpoints of the hypotenuse of a right-angled triangle are $(2, 0)$ and $(0, 2)$,find the locus of its third vertex.

What is the locus of the centroid of the triangle whose vertices are $(a \cos t, a \sin t)$,$(b \sin t, -b \cos t)$,and $(1, 0)$?