[" If the variable line "3x-4y+k=0" lies between the circles "x^(2)+y^(2)-2x-2y+1],[x^(2)+y^(2)-16x-2y+61=0" without intersecting or touching either circle,then the range of "],[" where "a,b in I." Find the value of "(b-a)" ."]

If the variable line 3x-4y+k=0 lies between the circles x^(2)+y^(2)-2x-2y+1=0 and x^(2)+y^(2)-16x-2y+61=0 without x^(2)+y^(2)-16x-2y+61=0 without intersecting or touching either circle,then the range of k is (a,b) where a,b in I Find the value of (b-a).

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 is a in(2sqrt(5)-15,0)a in(-oo,2sqrt(5)-15,)a in(0,-sqrt(5)-1)( d) a in(-sqrt(5)-1,oo)

If the variable line 3x + 4y= alpha lies between the two circles (x-1)^(2)+(y-1)^(2) = 1 and (x - 9)^(2) + (y-1)^(2) = 4 , without intercepting a chord on either circle, then the sum of all the integral values of alpha is__________

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 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 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)

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 .

If a variable line 3x+4y-lamda=0 is such that the two circles x^(2)+y^(2)-2x-2y+1=0 " and" x^(2)+y^(2)-18x-2y+78=0 are on its opposite sides, then the set of all values of lamda is the interval

if the line 3x-4y-k=0 touches the circle x^(2)+y^(2)-4x-8y-5=0 at (a,b), find (k+a+b)/5is