$\text{ If the normals to the curve }y=x^2\text{ at the points }P,Q\text{ and }R\text{ nass through the point }(0,3/2)\text{ then the radius of the }$

$\text{ circle circumscribing }\mathrm{\Delta }PQR\text{ is }$

$\text{ Equation of normal at any point }\left(t,t^2\right)\text{ is }$

$\begin{array}{l}y-t^2=-\frac{1}{2t}(x-t)\\ \text{ It passes through }\left(0,\frac{3}{2}\right)\\ \therefore t=0\text{ or }t=1,-1\end{array}$

$\text{ Hence }P,Q,R\text{ are }(0,0)(1,1)\text{ and }(-1,1)\text{ . }$

$\Rightarrow PQR\text{ is a right triangle. }$

$\therefore \text{ radius of circumcircle is }1.$