The two circles `x^(2)+y^(2)-2x-3=0` and `x^(2)+y^(2)-4x-6y-8=0` are such that

Prove the equation of the tangent from any point on the line 3x-8y+2=0 to the circles x^(2)+y^(2)+2x-10y+12=0 and x^(2)+y^(2)-4x+6y+8=0 are equal.

. The centres of the circles x^(2)+y^(2)-6x-8y-7=0 and x^(2)+y^(2)-4x-10y-3=0 are the ends of the diameter of the circle

If the two circles 2x^(2) +2y^(2) -3x+6y+k=0 and x^(2) +y^(2) -4x +10y +16=0 cut orthogonally, then the vlaue of k is-

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.

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.

Two circles x^(2) + y^(2) - 2x - 4y = 0 and x^(2) + y^(2) - 8y - 4 = 0