The locus of the centres of the circles,which cut the circles $x^2+y^2+4x-6y+9=0$ and $x^2+y^2-5x+4y+2=0$ orthogonally,is

If a chord is drawn from the origin to the circle $(x - 1)^2 + y^2 = 1$,then the equation of the locus of the midpoint of this chord is:

Two line segments $AB$ and $CD$ are constrained to move along the $X$ and $Y$-axes,respectively,in such a way that the points $A, B, C, D$ are concyclic. If $AB = a$ and $CD = b$,then the locus of the centre of the circle passing through $A, B, C, D$ in polar coordinates is

If $t \in R - \{-1\}$,then the locus of the point $\left(\frac{3at}{1+t^3}, \frac{3at^2}{1+t^3}\right)$ is

The locus of the centre of a circle touching both the coordinate axes is

The locus of the centre of the circle which cuts a chord of length $2a$ from the positive $x$-axis and passes through a point on the positive $y$-axis at a distance $b$ from the origin is: