Question

partial differential equation of plane all at constant distance k from the origin

Answer 1

Let the required equation of the plane be

z=lx+my+nlx+my−z+n=0.....(1)z=lx+my+nlx+my−z+n=0.....(1)

Now the plane (1)(1) is at constant distance aa from the origin

∴a=|n|l2+m2+1−−−−−−−−−√∴a=|n|l2+m2+1

⟹a=±nl2+m2+1−−−−−−−−−√⟹a=±nl2+m2+1

Here p=|ax1+by1+cz1+d|a2+b2+c