(c) Given points are A(2,3,4) and B(−2,3,4) and AB=4. Now let point P(x,y,z), such that PA+PB=4=AB means point P is collinear with points A and B and lies between them, so
x−2
2+2
=
y−3
3−3
=
z−4
4−4
⇒y−3=0=z−4 or (y−3)2+(z−4)2=0 ⇒y2+z2−6y−8z+25=0