$P(3,1)$,$Q(6,5)$ and $R(x,y)$ are three points such that the angle $\angle PRQ$ is a right angle and the area of the $\Delta RPQ = 5$. Then the number of such points $R$ is

The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is

If $P(\frac{\pi}{3})$ and $Q(\frac{2\pi}{3})$ represent two points on the circle $x^2+y^2-4x+6y-12=0$ in parametric form,then the length of the chord $PQ$ is

The set of all real values of $\lambda$ for which exactly two common tangents can be drawn to the circles $x^2 + y^2 - 4x - 4y + 6 = 0$ and $x^2 + y^2 - 10x - 10y + \lambda = 0$ is the interval:

If the chord $x+y=1$ of the circle $x^2+y^2=a^2$ subtends a right angle at the origin,then $a=$

If one of the diameters of the circle $x^2+y^2-2x-6y+6=0$ is a chord to a larger circle with center $(2,1)$,then the radius of the larger circle is: