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.
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!!