Given two circles `x^2 +y^2+3sqrt(2)(x+y)=0` and `x^2 +y^2 +5sqrt(2)(x+y)=0`. Let the radius of the third circle, which touches the two given circles and to their common diameter, be `(2lambda-1)/lambda` The value of `lambda` is

Let the equation of the circle is x^(2) + y^(2) = 25 and the equation of the line x + y = 8 . If the radius of the circle of maxium area and also touches x + y = 8 and x^(2) + y^(2) = 25 is (4sqrt(2) + 5)/(lambda) . Then the value of lambda is.

If two circleS x^(2)+y^(2)+2 lambda x+c=0 and x^(2)+y^(2)-2 mu y-c=0 have equal radius then the locus of (lambda, mu) is

If a circle passes through the points of intersection of the coordinate axes with the lines lambda x-y+1=0 and x-2y+3=0 then the value of lambda is.........

If the circles x^(2) + y^(2) - 2lambda x - 2y - 7 = 0 and 3(x^(2) + y^(2)) - 8x + 29y = 0 are orthogonal then lambda =

If the two circles (x-2)^(2)+(y+3)^(2) =lambda^(2) and x^(2)+y^(2) -4x +4y-1=0 intersect in two distinct points then :

If the two circles (x-2)^(2)+(y+3)^(2) =lambda^(2) and x^(2)+y^(2) -4x +4y-1=0 intersect in two distinct points then :