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.

lf the circle x^(2)+y^(2)=2 and x^(2)+y^(2)-4x-4y+lamda=0 have exactly three real common tangents then lamda=

If (-1/3,-1) is a centre of similitude for the circles x^2+y^2=1 and x^2+y^2-2x-6y-6=0 , then the length of common tangent of the 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 5sqrt3/2

The common tangents to the circles x^2 + y^2 + 2x =0 and x^2 + y^2-6x=0 form a triangle which is

Find the coordinates of the point at which the circles x^2+y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

the no. of possible integral values of m for which the circle x^2+y^2=4 and x^2+y^2-6x-8y+m^2=0 has exactly two common tangents are