Consider the family ol circles `x^2+y^2=r^2, 2 < r < 5` . If in the first quadrant, the common tangnet to a circle of this family and the ellipse `4x^2 +25y^2=100` meets the co-ordinate axes at A and B, then find the equation of the locus of the mid-point of AB.

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0 . The distance between the points A and B , is

Consider the family of circles x^2+y^2-2x-2lambday-8=0 passing through two fixed points Aa n dB . Then the distance between the points Aa n dB is_____

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0 . If the circle x^(2)+y^(2)-10x+2y=c=0 is orthogonal to S=0 , then the value of c is

The orthogonal trajectories of the family of circles given by x^2 + y^2 - 2ay = 0 , is

The centre of family of circles cutting the family of circles x^2 + y^2 + 4x(lambda-3/2) + 3y(lambda-4/3)-6(lambda+2)=0 orthogonally, lies on

Total number of lines touching atleast two circles of the family of four circles x^(2) + y^(2) +- 8x +- 8y = 0 is

Find the differential equation of the family of concentric circles x^2+y^2=a^2 .

Consider a family of circles passing through the point (3,7) and (6,5). Answer the following questions. If each circle in the family cuts the circle x^(2)+y^(2)-4x-6y-3=0 , then all the common chords pass through the fixed point which is

A circle S= 0 passes through the common points of family of circles x^2 +y^2 +lambdax-4y +3=0 and (lambda epsilon R) has minimum area then

The area bounded by circles x^2 +y^2=r^2 , r = 1, 2 and rays given by 2x^2-3xy-2y^2=0 ,is