The number of common tangents to the circles ${x^2} + {y^2} - x = 0$ and ${x^2} + {y^2} + x = 0$ is:

The equation of the circle inscribed in a square formed by the lines $x+y-2=0$,$x+y-6=0$,$x-y+1=0$ and $x-y+5=0$ is

From three non-collinear points,we can draw:

Let $M\left(\frac{-7}{2}, \frac{-5}{2}\right)$ be the midpoint of the chord $AB$ of the circle $x^2+y^2+10x+8y-23=0$. If $ax+by+1=0$ is the equation of $AB$,then $3a+3b=$

The straight line $2x - 3y = 1$ divides the circular region $x^2 + y^2 \leq 6$ into two parts. If $S = \left\{ \left(2, \frac{3}{4}\right), \left(\frac{5}{2}, \frac{3}{4}\right), \left(\frac{1}{4}, -\frac{1}{4}\right), \left(\frac{1}{8}, \frac{1}{4}\right) \right\}$,then the number of point$(s)$ in $S$ lying inside the smaller part is

The line $x+y+1=0$ intersects the circle $x^2+y^2-4x+2y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the midpoint of $AB$,then $a-b=$