The circles `x^2+y^2-12 x-12 y=0` and `x^2+y^2+6x+6y=0.` touch each other externally touch each other internally intersect at two points none of these

If the circles x^2 + y^2 + 2ax + b = 0 and x^2+ y^2+ 2cx + b = 0 touch each other (a!=c)

Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+4y-1=0 (a)touch internally (b)touch externally (c)have 3x+4y-1=0 as the common tangent at the point of contact (d)have 3x+4y+1=0 as the common tangent at the point of contact

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 curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) touch each other (b) cut orthogonally intersect at 45^0 (d) intersect at 60^0

The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) touch each other (b) cut orthogonally intersect at 45^0 (d) intersect at 60^0

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

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then, a. C1 and C2 touch each other at one point b. C1 and C2 touch each other exactly at two point c. C1 and C2 intersect(but do not touch) at exactly two point d. C1 and C2 neither intersect nor touch each other

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If x^2-2p x y-y^2=0 and x^2-2q x y-y^2=0 bisect angles between each other, then find the condition.