Question

A plane passes through the point $P(4,0,0)$ and $Q(0,0,4)$ and is parallel to the $y$-axis. The distance of the plane from the origin is

• A. $2$
• B. $4$
• C. $\sqrt{2}$
• D. $2\sqrt{2}$

Answer 1

The correct option is D $2\sqrt{2}$

General equation of a plane parallel to $y$-axis is given by,
$ax+bz+c=0$
Since this plane is also passes through $(4,0,0)$ and $(0,0,4)$
$\Rightarrow 4a+c=0\Rightarrow a=-\frac{c}{4}$
and $4b+c=0\Rightarrow b=-\frac{c}{4}$
Hence, required plane is,
$x+z-4=0$
Therefore distance of origin from this plane is
$=d=\left|\frac{-4}{\sqrt{1^2+1^2}}\right|=2\sqrt{2}$