Question

The equation to the plane through the points $(2,3,1)$ and $(4,-5,3)$ parallel to $x-$ axis is

• A. $x+y+4z=7$
• B. $x+4z=7$
• C. $y-4z=7$
• D. $y+4z=-7$
• E. $y+4z=7$

Answer 1

Answer: (E)

We know that the equation of a plane parallel to $x-$ axis is $by+cz+d=0$ Since, it passes through the points (2 3 1) and $(4,-5,3)$ .
$\therefore$ $3b+c+d=0$ ..(i) and $-5b+3c+d=0$ ...(ii)
On solving Eqs. (i) and (ii), we get
$\frac{b}{1-3}=\frac{c}{-8}=\frac{d}{14}$
$\Rightarrow$ $\frac{b}{-2}=\frac{c}{-8}=\frac{d}{14}$
$\therefore$ Equation of plane is
$-2y-8z+14=0$
$\Rightarrow$ $y+4z=7$