Prove that the following pairs of circles intersect orthogonally :
`x^(2) +y^(2) - 2ax + c = 0 and x^(2) + y^(2) + 2by - c = 0`

If two circles x^(2) + y^(2) - 2ax + c = =0 and x^(2) + y^(2) - 2by + c = 0 touch each other , then c =

The locus of the centers of the circles which cut the circles x^(2) + y^(2) + 4x – 6y + 9 = 0 and x^(2) + y^(2) – 5x + 4y – 2 = 0 orthogonally is

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)) .

The equation of the circle which pass through the origin and cuts orthogonally each of the circles x^(2)+y^(2)-6x+8=0 and x^(2)+y^(2)-2x-2y-7=0 is

Which of the following pair(s) of curves is/are orthogonal? y^(2)=4ax;y=e^(-(1)/(2))y^(2)=4ax;x^(2)=4ayat(0,0)xy=a^(2);x^(2)-y^(2)=b^(2)y=ax;x^(2)+y^(2)=c^(2)

If circles x^(2) + y^(2) + 2gx + 2fy + c = 0 and x^(2) + y^(2) + 2x + 2y + 1 = 0 are orthogonal , then 2g + 2f - c =

Equation of the circle which cuts each of the circles x ^(2) + y ^(2) + 2gx + c =0, x ^(2) + y ^(2) + 2g _(1) x +c =0 and x ^(2) + y^(2) + 2hx + 2ky + a=0 orthogonally is