If a line through P(-2,3) meets the circle `x^(2)+y^(2)-4x+2y+k=0` at A and B such that PA.PB =31 then the radius of the circle is

The line 2x-y+6=0 meets the circle x^(2)+y^(2)-2y-9=0 at A and B. Find the equation of the circle on AB as diameter.

A line is drawn through the point P(3,11) to cut the circle x^(2)+y^(2)=9 at A and B. Then PA.PB is equal to

The tangents to the circle x^(2)+y^(2)-4x+2y+k=0 at (1,1) is x-2y+1=0 then k=

If the line ax+by+11=0 meets the circle x^(2)+y^(2)=61 at A,B and P(-5,6) is on the circle such that PA=PB=10 then |a+b|=

A line drawn through the point P(4,7) cuts the circle x^(2)+y^(2)=9 at the points A and B .Then PA.PB is equal to:

If a line with positive alope passing through P(0,1) intersects the curve y=x^(2)-x at A=P that PA.PB=2, then AB is

Lines are drawn through the point P(-2,-3) to meet the circle x^(2)+y^(2)-2x-10y+1=0 The length of the line segment PA,A being the point on the circle where the line meets the circle at coincident points,is 4sqrt(k) then k is

If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0at A and B, then themaximum of PA+PB is