If a circle passing through $(1, -2)$ has $x - y = 2$ and $2x + 3y = 14$ as its diameters,then the radius of the circle is

The centre of the circle $r^2-4r(\cos \theta+\sin \theta)-4=0$ in Cartesian coordinates is

The equation of the circle which touches both axes and whose centre is $({x_1}, {y_1})$ is

The points $(1,0), (0,1), (0,0)$ and $(2k, 3k), k \neq 0$ are concyclic,if $k$ is

Let $P(x_1, y_1)$ and $Q(x_2, y_2)$ be two points such that their abscissae $x_1$ and $x_2$ are the roots of the equation $x^2 + 2x - 3 = 0$,while the ordinates $y_1$ and $y_2$ are the roots of the equation $y^2 + 4y - 12 = 0$. The centre of the circle with $PQ$ as diameter is

Let $\alpha, \beta$ be the roots of $x^2+5x+6=0$ and $\gamma, \delta$ be the roots of $y^2+6y+7=0$. Then the equation of the circle with $(\alpha, \gamma)$ and $(\beta, \delta)$ as the extremities of a diameter is