A circle `S` of radius `' a '` is the director circle of another circle `S_1,S_1` is the director circle of circle `S_2` and so on. If the sum of the radii of all these circle is 2, then the value of `' a '` is (a) `2+sqrt(2)` (b) `2-1/(sqrt(2))` (c) `2-sqrt(2)` (d) `2+1/(sqrt(2))`

A circle x^2 +y^2 + 4x-2sqrt2 y + c = 0 is the director circle of circle S_1 and S_1 is the director circle of circle S_2 , and so on. If the sum of radii of all these circles is 2, then find the value of c.

A circle x^2+y^2+4x-2sqrt(2)y+c=0 is the director circle of the circle S_1a n dS_1 is the director circle of circle S_2, and so on. If the sum of radii of all these circles is 2, then the value of c is ksqrt(2) , where the value of k is___________

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The radius of the circle passing through the points (1, 2), (5, 2) and (5, -2) is : (A) 5sqrt(2) (B) 2sqrt(5) (C) 3sqrt(2) (D) 2sqrt(2)

The radius of the director circle of the hyperbola x^2//25-y^(2)//9=1 is

Maximum value of |z+1+i|, where z in S is (a) sqrt(2) (b) 2 (c) 2sqrt(2) (d) 3sqrt(2)

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is (a) 3sqrt(5) (b) 5sqrt(3) (c) 2sqrt(5) (d) 5sqrt(2)

The director circle of a hyperbola is x^(2) + y^(2) - 4y =0 . One end of the major axis is (2,0) then a focus is (a) (sqrt(3),2-sqrt(3)) (b) (-sqrt(3),2+sqrt(3)) (c) (sqrt(6),2-sqrt(6)) (d) (-sqrt(6),2+sqrt(6))

Find the equation of the circle with centre : (-a , b) and radius sqrt(a^2-b^2) .

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 2sqrt(2)-1 (d) 1