Mathematics - Parabola Question with Solution | TestHub

Both the curves are symmetrical about the line $y=x$. Distance between any pair of points $=2\{$ distance of $\left(t,t^2+1\right)$ from $y=x]$

$$\begin{array}{rlrl}& 2\left[\frac{t^2+1-t}{\sqrt{2}}\right]=\sqrt{2}\left[t^2-t+1\right]& \mathrm{Min}{t}^2-t+1=-\left[\frac{1-4}{4}\right]=\frac{3}{4}& \Rightarrow \frac{3\sqrt{2}}{4}\end{array}$$