The equation of plane through line of intersection of planes ax+by+cz+d=0 , a`x+b`y+c`z+d`=0 and parallel to line y=0,z=0 is??

Equation of any plane through the line of intersection of the given two planes

ax+ by+ cz+ d=0 and  a′x+ b′y+ c′z+ d′=0 is given by

(ax+by+cz+d) + λ(a′x+b′y+c′x+d′)=0

 

(a+λa′)x+(b+λb′)y+(c+λc′)z+(d+λd′)=0

But given that this plane is parallel to the line y=0,z=0y=0,z=0 (which is xaxis).

The normal n→=(a+λa′,b+λb′,c+λc′) is perpendicular to the line.( i.e., xaxis.)

(a+λa′,b+λb′,c+λc′).(1,0,0)=0
a+λa′=0orλ=−aa′
Substituting the value of λ we get the required eqn. of the plane is
(ab′−a′b)y+(bc′−b′c)z+(ac′−a′c)=0