Two rods of lengths `a` and `b` slide along the `x`-axis and `y`-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is:

Options

A. `4 (x ^(2) + y ^(2)) =a ^(2) +b ^(2)`
B. `x ^(2) + y ^(2) =a ^(2) +b ^(2)`
C. `4(x ^(2) -y ^(2)) =a ^(2) -b ^(2)`
D. `x ^(2) -y ^(2)=a ^(2) -b ^(2)`

Answer

C