Find the range of parameter a for which the variable line `y=2x+a` lies between the circles `x^(2)+y^(2)-2x-2y+1=0` and `x^(2)+y^(2)-16x-2y+61=0` without intersecting or touching either circle.

The range of parameter ' a ' for which the variable line y=2x+a lies between the circles x^2+y^2-2x-2y+1=0 and x^2+y^2-16 x-2y+61=0 without intersecting or touching either circle is a in (2sqrt(5)-15 ,0) a in (-oo,2sqrt(5)-15 ,) a in (0,-sqrt(5)-10) (d) a in (-sqrt(5)-1,oo)

The range of parameter ' a ' for which the variable line y=2x+a lies between the circles x^2+y^2-2x-2y+1=0 and x^2+y^2-16 x-2y+61=0 without intersecting or touching either circle is (a) a in (2sqrt(5)-15 ,0) (b) a in (-oo, 2sqrt(5)-15,) (c) a in (2sqrt(5)-15,-sqrt(5)-1) (d) a in (-sqrt(5)-1,oo)

The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each other

Number of integral values lambda for which the varaible line 3x+4y-lambda = 0 lies between the circles x^2 + y^2 - 2x - 2y + 1 = 0 and x^2 + y^2 - 18x - 2y + 78 = 0 , without intersecting any circle at two distinct points.

Find number of integral values of k for which the line 3x + 4y - k = 0 , lies between the circles x^2 + y^2 - 2x - 2y + 1 = 0 and x^2 + y^2 - 18 x - 12 y + 113 = 0 , without cutting a chord on either of circle.

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

The number of common tangents of the circles x^(2) +y^(2) =16 and x^(2) +y^(2) -2y = 0 is :

The angle of intersection of the circles x^(2)+y^(2)=4 and x^(2)+y^(2)+2x+2y , is

If the circles x^(2)+y^(2)=a^(2), x^(2)+y^(2)-6x-8y+9=0 touch externally then a=