Let `C_1 and C_2` are circles defined by `x^2+y^2 -20x+64=0` and `x^2+y^2+30x +144=0`. The length of the shortest line segment PQ that is tangent to `C_1` at P and to `C_2` at Q is

The circles x^(2) +y^(2) + 2ax +c =0 and x^(2) +y^(2) +2bx +c =0 have no common tangent if

Let C_1 and C_2 be two circles whose equations are x^2+y^2-2x=0 and x^2+y^2+2x=0 and P(lambda, lambda) is a variable point

Let C_(1) and C_(2) be the circles x^(2) + y^(2) - 2x - 2y - 2 = 0 and x^(2) + y^(2) - 6x - 6y + 14 = 0 respectively. If P and Q are points of intersection of these circles, then the area (in sq. units ) of the quadrilateral PC_(1) QC_(2) is :

Let C_(1) and C_(2) be two circles whose equations are x^(2)+y^(2)-2x=0 and x^(2)+y^(2)+2x=0 and P(lambda,lambda) is a variable point

Let C_(1) and C_(2) denote the centres of the circles x^(2) +y^(2) = 4 and (x -2)^(2) + y^(2) = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C_(1) PQ and C_(2) PQ are in the ratio _

The value of c, for which the line y=2x+c is a tangent to the circle x^2+y^2=16 , is