The set of points on the axis of the parabola $y^2-4x-2y+5=0$ from which all the three normals to the parabola are real is

$y^2-2y=4x-5$

$y^2-2y+1=4x-4$

${(y-1)}^2=4(x-1)$

axis of the parabola is $y-1=0$

$y=1$

$\Rightarrow x-1>2a$

$\Rightarrow \left(\begin{array}{l}\because 4a=4\\ a=1\end{array}\right)$

$x-1>2$

$x>3$

$\therefore$ The number of point is $(k,1)$ where $k>3$ 

Concept:- If three normals to axy parabola $y^2=4ax$ from a given point $(\lambda ,k)$ be real real  $h>2a$