The radical axis of two circles and the line joining their centres are:

If the inverse point of the point $P(3, 3)$ with respect to the circle $x^2+y^2-4x+4y+4=0$ is $Q(a, b)$,then $a+5b=$

The centre of the circle passing through the point $(0, 1)$ and touching the curve $y = x^2$ at $(2, 4)$ is

If $\theta$ is the angle between the circles $x^2+y^2-4x+2y-4=0$ and $x^2+y^2-2x+4y-11=0$,then $\sin \theta=$

Two circles each of radius $5 \text{ units}$ touch each other at the point $(1, 2)$. If the equation of their common tangent is $4x + 3y = 10$,and $C_{1}(\alpha, \beta)$ and $C_{2}(\gamma, \delta)$,$C_{1} \neq C_{2}$ are their centres,then $|(\alpha + \beta)(\gamma + \delta)|$ is equal to .... .

The number of possible common tangents that can be drawn to the circles $x^2+y^2+4x-6y-3=0$ and $x^2+y^2+4x-2y+1=0$ is