Statement 1 : Circles `x^2+y^2=144` and `x^2+y^2-6x-8y=0` do not have any common tangent. Statement 2 : If two circles are concentric, then they do not hav common tangents.

Statement 1 : The number of common tangents to the circles x^(2) + y^(2) =4 and x^(2) + y^(2) -6x - 6y = 24 is 3. Statement 2 : If two circles touch each other externally thenit has two direct common tangents and one indirect common tangent.

Statement 1 : The number of common tangents to the circles x^(2) +y^(2) -x =0 and x^(2) +y^(2) +x =0 is 3. Statement 2 : If two circles touch each other externally then it has two direct common tangents and one indirect common tangent.

STATEMENT-1 : Let x^(2) + y^(2) = a^(2) and x^(2) + y^(2) - 6x - 8y -11 = 0 be two circles. If a = 5 then two common tangents are possible. and STATEMENT-2 : If two circles are intersecting then they have two common tangents.

Let S_(1) : x^(2) + y^(2) = 25 and S_(2) : x^(2) + y^(2) - 2x -2y - 14 = 0 be two circles. STATEMENT-1 : S_(1) and S_(2) have exactly two common tangents. and STATEMENT-2 : If two circles touches each other internally they have one common tangent.

Consider the circles x^(2) + y^(2) = 1 & x^(2) + y^(2) – 2x – 6y + 6 = 0 . Then equation of a common tangent to the two circles is

The circles x^(2)+y^(2)+2x+4y-20=0 and x^(2)+y^(2)+6x-8y+10=0 a) are such that the number of common tangents on them is 2 b) are orthogonal c) are such that the length of their common tangents is 5((12)/(5))^((1)/(4)) d) are such that the length of their common chord is 5(sqrt(3))/(2)

If the two circles x^(2) + y^(2) =4 and x^(2) +y^(2) - 24x - 10y +a^(2) =0, a in I , have exactly two common tangents then the number of possible integral values of a is :