Statement 1:  Through $(a,a+1)$ there cannot be more than one normal to parabola $y^2=4x$ if $a<2.$

Statement 2: The point $(a,a+1)$ is outside the parabola for all $\lambda \ne 1$   

Any normal to Parabola $y^2=4x$ is $y+tx=2t+t^3$

If it passes through $(a,a+1)$ we get $t^3+t(2-a)-a-1=0$ 

Let $f\left(t\right)=t^3+t(2-a)-a-1=0$

$f\text{'}\left(t\right)=3t^2+2-a>0fora<2$

$\therefore f\left(t\right)$has only one real root.

Statement 2 is also True as ${(a+1)}^2>4a$ for $a\ne 1$ but Statement 2 is not used to solve Statement 1