Answer
$\dfrac{-5}{4}, \dfrac{-5}{4},\dfrac{25}{8}$
Work Step by Step
Our aim is to determine the normal line equation.
The general form is:
$\dfrac{(x_2-x_1)}{f_x(x_1,y_1,z_1)}=\dfrac{(y_2-y_1)}{f_y(x_1,y_1,z_1)}=\dfrac{(z_2-z_1)}{f_x(x_1,y_1,z_1)}$ ...(1)
From the given data, we have $f(x,y,z)=(1,1,2)$
Equation (1), becomes:
Thus,
$\dfrac{(x-1)}{2}=\dfrac{(y-1)}{2}=\dfrac{(z-2)}{-1}$
Consider
$\dfrac{(x-1)}{2}=\dfrac{(y-1)}{2}=\dfrac{(z-2)}{-1}=s$
Therefore, $x=1+3s;y=1+2s,z=2-s$
Simplify to get the value of $s$, we have $s=-\dfrac{9}{8}$
Equation of a paraboloid is: $z=x^2+y^2$
This yields $x=\dfrac{-5}{4},y=\dfrac{-5}{4},z=\dfrac{25}{8}$
