The locus of the centre of the circles which touches both the axes is given by

Options

A. `x^(2)-y^(2)=0`
B. `x^(2)+y^(2)=0`
C. `x^(2)-y^(2)=1`
D. `x^(2)+y^(2)=1`

Answer

A

Explanation

Let (h, k) be the centre of a circle touching both the axes and r be its radius. Then,
`|h|=r and |k|=r`
`rArr |h|=|k|rArrh = pm k`
Hence, the locus (h, k) is `x=pmy` or, `x pm y = 0`.
the combined equation of these two lines is
`(x+y)(x-y)=0` or, `x^(2)-y^(2)=0`.