A curve passes through the point $P(1,2,3).$ If at the point $P,=\frac{1}{4}$ and hat$(N)=($:$0,-1,0$:$),$ then what is the radius and the center of the osculating circle at this point?

$x-1=0$

$y-2=-1y=1$

$IfCis$ the center $of$ the circle, then $z-3=0z=3$

vec$(PC)=($:$0,-4,0).$

If $f(x,y)=x$ Hence $C(1,-2,3)$