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^2-2x-2lambda-8=0 passing through two fixed points Aa n dB . Then the distance between the points Aa n dB is_____

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

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

Using integration find the area of the circle x^2+y^2= r^2 .

The area of the circle x^2+y^2=a^2 is :

Consider a family of circles which are passing through the point (-1,1) and are tangent to the x-axis. If (h ,k) are the coordinates of the center of the circles, then the set of values of k is given by the interval. (a) kgeq1/2 (b) -1/2lt=klt=1/2 klt=1/2 (d) 0 < k < 1/2

Consider the two circles C_(1):x^(2)+y^(2)=a^(2)andC_(2):x^(2)+y^(2)=b^(2)(agtb) Let A be a fixed point on the circle C_(1) , say A(a,0) and B be a variable point on the circle C_(2) . The line BA meets the circle C_(2) again at C. 'O' being the origin. If (OA)^(2)+(OB)^(2)+(BC)^(2)=lamda," then "lamdain

Consider the family of lines 5x+3y-2+lambda_(1)(3x-y-4)=0 " and " x-y+1+lambda_(2)(2x-y-2)=0 . Find the equation of a straight line that belongs to both the families.

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

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S. The radius of the circumcircle of the triangle PRS is-