Prove that the circle `x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0` touch each other if
`(1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2))` .

If two circles x^(2)+y^(2)+c^(2)=2ax and x^(2)+y^(2)+c^(2)-2by=0 touch each other externally , then prove that (1)/(a^(2))+(1)/(b^(2))=(1)/(c^(2))

If circles x^(2) + y^(2) + 2g_(1)x + 2f_(1)y = 0 and x^(2) + y^(2) + 2g_(2)x + 2f_(2)y = 0 touch each other, then

Prove that the circles x^(2)+y^(2)+2ax+ay-3a^(2)=0andx^(2)+y^(2)-8ax-6ay+7a^(2)=0 touch each other.

If the circles x^(2)+y^(2)+2ax+c=0andx^(2)+y^(2)+2by+c=0 touch each other then show that (1)/(a^(2)),(1)/(2c),(1)/(b^(2)) are in A.P.

Two circles centres A and B radii r_1 and r_2 respectively. (i) touch each other internally iff |r_1 - r_2| = AB . (ii) Intersect each other at two points iff |r_1 - r_2| ltAB lt r_1 r_2 . (iii) touch each other externally iff r_1 + r_2 = AB . (iv) are separated if AB gt r_1 + r_2 . Number of common tangents to the two circles in case (i), (ii), (iii) and (iv) are 1, 2, 3 and 4 respectively. circles x^2 + y^2 + 2ax + c^2 = 0 and x^2 + y^2 + 2by + c^2 = 0 touche each other if (A) 1/a^2 + 1/b^2 = 2/c^2 (B) 1/a^2 + 1/b^2 = 2/c^2 (C) 1/a^2 - 1/b^2 = 2/c^2 (D) 1/a^2 - 1/b^2 = 4/c^2

The two circles x^(2)+y^(2)=ax and x^(2)+y^(2)=c^(2)(c gt 0) touch each other, if |(c )/(a )| is equal to

The two circles x^(2)+y^(2)=ax, x^(2)+y^(2)=c^(2) (c gt 0) touch each other if

The two circles x^(2)+y^(2)-cx=0 and x^(2)+y^(2)=4 touch each other if:

The condition that the circles x^(2)+y^(2)+2ax+c=0, x^(2)+y^(2)+2by+c=0 may touch each other is

The condition that the circles x^(2)+y^(2)+2ax+c=0, x^(2)+y^(2)+2by+c=0 may touch each other is