[" ler the family of circle "x^(2)+y^(2)=r^(2),2

Consider the family ol circles x^(2)+y^(2)=r^(2),2

Find the differential equation of the family of circles (x-a)^(2)+(y-b)^(2)=r^(2) , where 'a' and 'b' are arbitrary constants.

Find the differential equation of the family of circles x^(2) + y^(2) = 2ay , where a is a parameter .

Find the differential equation of the family of circles x^(2) + y^(2) = 2ax , where a is a parameter .

The differential equation representing the family of circles x^(2)+(y-a)^(2)=a^(2) will be of order two.

Consider the family of 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= r^2 2 lt r lt 5 . If in the first quadrant, the common tangent to a circle of this family and the ellipse frac{x^(2)}{25} +frac{y^(2)}{4} =1 meets the axes at A and B then find the equation of the locus of middle point of AB.

Consider the family of 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.

Find the orthogonal of the family of circles x^(2) + y^(2) = 2ax each of which touches the y-axis at origin.

The differential equation for the family of circle x ^(2) + y ^(2) - 2ay =0 where a is an arbitary constant is :