If the sum of the squares of the distance of the point (x, y, z) from the points (a, 0, 0) and (-a, 0, 0) is 2c2, then which one of the following is correct?

[b] Let the point be P(x, y, z) and two points, (a, 0, 0) and (-a, 0, 0) be A and B As given in the problem, PA2+PB2=2c2 So, (x+a)2+(y−0)2+(z−0)2 +(x−a)2+(y−0)2+(z−0)2=2c2 or, (x+a)2+y2+z2+(x−a)2+y2+z2=2c2 x2+2a+a2+y2+z2+x2−2a+a2+y2+z2=2c2⇒2(x2+y2+z2+a2)=2c2 ⇒x2+y2+z2+a2=c2 ⇒x2+a2=c2−y2−z2