If the radii of the circles `(x-1)^2+(y-2)^2=1` and `(x-7)^2+(y-10)^2=4` are increasing uniformly w.r.t. time as 0.3 units/s and 0.4 unit/s, respectively, then at what value of `t` will they touch each other?

The two circles x^2+y^2=ax and x^2+y^2=c^2 (cgt0) touch each other if

The area bounded by the parabolas y=(x+1)^2 and y=(x-1)^2a n dy=(x-1)^2 and the line y=1/4 is (a)4 sq. units (b) 1/6 sq. units 4/3 sq. units (d) 1/3 sq. units

If the circle x ^(2) +y^(2) -4rx- 2ry+4r^(2)=0 and x^(2) +y^(2) =25 touch each other, then r satisfies-

The circle x ^(2) +y^(2) -8 x+4=0 touches -

If the circles x ^(2) +y^(2) +2gx +2fy =0 and x ^(2) +y^(2) +2g'x+ 2f'y=0 touch each other then-

Statement 1 : The least and greatest distances of the point P(10 ,7) from the circle x^2+y^2-4x-2y-20=0 are 6 units and 15 units, respectively. Statement 2 : A point (x_1,y_1) lies outside the circle S=x^2+y^2+2gx+2fy+c=0 if S_1>0, where S_1=x_1^2+y_1^2+2gx_1+2fy_1+c (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 +y^2=16 and x^2+y^2=1 . Then

One end of a diameter of the circle x^2+y^2-3x+5y-4=0 is (2,1). Find the coordinates of the other end.

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___________

If the circles x^2+y^2-9=0 and x^2+y^2+2alphax+2y+1=0 touch each other, then alpha is (a) -4/3 (b) 0 (c) 1 (d) 4/3