At what points on the curve `x^(2)+y^(2)-2x-4y+1=0`, the tangents are parallel to the Y-axis ?

Explanation

We know that force on current I carrying conductor placed in magnetic field B is,
`F=BxxI*dl`
`F=BIdlsintheta`
The direction of magnetic field at `O_(2)` due to the current `I_(1)` is parallel to y-axis and in y-direction.
As wire of current `I_(2)` is parallel to y-axis, current in `I_(2)` is also along y-axis. So `I_(2)andB_(1)` (magnetic field due to current `I_(1)`) are also along y-axis. i.e. angle between `I_(2)andB_(1)` is zero.
So, magnetic force `F_(2)` on the wire of current `I_(2)` is, `F_(2)=B_(1)I_(2)dlsin0^(@)`
`F_(2)=0`
Hence, force on `O_(2)` due to wire of current `I_(1)` is zero.