Question

Find the equation of the plane with intercept 4 on Z-axis and parallel to $XY$ plane.

Answer 1

Given that the plane has intercept $4$ on z-axis and is parallel to $XY$ plane

Since the required plane is parallel to $XY$ plane, the $x$-intercept and the $y$-intercept of the required plane is Infinite because the required plane does not intersect the $x$ and $y$ axis.

We know that the equation of plane whose intercepts are $a,b,c$ is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

$⟹\frac{x}{\infty }+\frac{y}{\infty }+\frac{z}{4}=1$

$⟹z=4$

Therefore the equation of required plane is $z=4$