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

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

If circles x^(2) + y^(2) + 2gx + 2fy + c = 0 and x^(2) + y^(2) + 2x + 2y + 1 = 0 are orthogonal , then 2g + 2f - c =

Let C be the circle concentric with the circle , 2x^(2) + 2y^(2) - 6x - 10 y = 183 and having area ((1)/(10))^(th) of the area of this circle. Then a tangent to C, parallel to the line, 3x + y = 0 makes an intercept on the y-axis , which is equal to :