If the circles of same radius `a` and centers at `(2, 3) and (5, 6)` cut orthogonally, then find `a.`

If two circles of the same radius r and centres at (-1,2) and (3,6) respectively cut orthogonally,then the value of r is

If the curves ay+x^(2)=7 and x^(3)=y cut orthogonally at (1,1), then find the value a .

Two circles with centres C_(1),C_(2) and same radius r cut each other orthogonally,then r is

The radius of the of circle touching the line 2x+3y+1=0 at (1,-1) and cutting orthogonally the circle having line segment joining (0,3) and (-2,-1) as diameter is

If a circle passes through the point (3,4) and cuts the circle x ^(2) + y ^(2) =a ^(2) orthogonally, the equation of the locus of its centre is

If two circles each of unit radius intersect orthogonally,the common area of the circles is