The foot of the perpendicular drawn from the origin to the plane is $(4,-2,5)$, then the Cartesian equation…
The foot of the perpendicular drawn from the origin to the plane is $(4,-2,5)$, then the Cartesian equation of the plane is
4x-2y+5z=45
-4x+2y+5z=45
4x-2y+5z+45=0
4x+2y-5z+45=0
Solution
Substitute $x=4, y=-2, \mathrm{z}=5$ in all options.
$\therefore \quad$ For option A
$\begin{aligned}
4 x-2 y+5 z & =4(4)-2(-2)+5(5) \\
& =16+4+25 \\
& =45
\end{aligned}$
$\therefore \quad$ Only option A is satisfied by $(4,-2,5)$