Find the locus of the centre of the circle touching the line `x+2y=0 and x=2y`

Explanation

Let (h,k) be the center


As it touches `x+2y=0 and x=2y` line
Then distance from center to both lines will be equal

`|(​h+2k)/sqrt(5)​|=
|(​h−2k)/sqrt(5)​|=Radius`

=`h+2k=+-h-2k`

`k=0 or h=0`

Locus of (h,k) is x=0 or y=0

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