Answer
$\dfrac{-5}{4}, \dfrac{-5}{4},\dfrac{25}{8}$
Work Step by Step
Formula to calculate normal line equation is:
$\dfrac{(x_2-x_1)}{f_x(x_1,y_1,z_1)}=\dfrac{(y_2-y_1)}{f_y(x_1,y_1,z_1)}=\dfrac{(z_2-z_1)}{f_x(x_1,y_1,z_1)}$
At point$(1,1,2)$
$\dfrac{(x-1)}{2}=\dfrac{(y-1)}{2}=\dfrac{(z-2)}{-1}$
Consider
$\dfrac{(x-1)}{2}=\dfrac{(y-1)}{2}=\dfrac{(z-2)}{-1}=k$
Therefore, $x=1+3k;y=1+2k,z=2-k$
After simplifications we get $t=-\dfrac{9}{8}$
Plug $t=-\dfrac{9}{8}$ in the equation of a paraboloid : $z=x^2+y^2$
The desired points are: $\dfrac{-5}{4}, \dfrac{-5}{4},\dfrac{25}{8}$
