please explain Q5 of Ex:12.2 of NCERT textbook. i went through the solution yet not able to understand......

its very important !!!!!!! reply soon

In the said question, we have to find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10 i.e., PA + PB = 10.

Solution:

In order to find the equation of the set of points P, firstly we consider the coordinates of P be (x, y, z).

The coordinates of points A and B are (4, 0, 0) and (–4, 0, 0) respectively.

It is given that PA + PB = 10.

Now, by using distance formula, we get

Simply on squaring both sides, we obtain

Again, on squaring both sides again, we get

25 (x² + 8x + 16 + y² + z²) = 625 + 16x² + 200x

⇒ 25x² + 200x + 400 + 25y² + 25z² = 625 + 16x² + 200x

⇒ 9x² + 25y² + 25z² – 225 = 0

Thus, the required equation is 9x² + 25y² + 25z² – 225 = 0.

Hope you get it now!!