 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says, find the equation of the set of points P, the sum of whose distance is from the point A that is 400 and the point B that is minus 400 is equal to 10. Before starting with the solution, let us see the key idea behind the question that is if a point P that is x1, y1, z1 and a point Q, x2, y2, z2 are two points then the distance between them that is PQ is given by the square root of x2 minus x1 the whole square plus y2 minus y1 the whole square plus z2 minus z1 the whole square. Let us start with the solution to this one now. Here we are given two points this and this. Let a point P given by the coordinates x, y and z be the required point. Now distance between the point P and A is given by P A that is equal to square root of the whole square plus y minus 0 the whole square plus z minus 0 the whole square this is equal to minus 4 the whole square plus y square plus z square. Similarly we see that P B that is distance between the point B and the point P is given by the square root of the whole square because x minus minus 4 is x plus 4 plus y minus 0 the whole square plus z minus 0 the whole square this is equal to square root of x plus 4 the whole square plus y square plus z square. Since it is given to us in the question that P A plus P B is equal to 10 that means distance between P and the point A plus distance between P and the point B is equal to 10 therefore we can say that square root plus y square plus z square y square plus z square is equal to 10 4 the whole square plus y square plus z square is equal to 10 minus plus y square plus z square both sides plus y square plus z square is equal to 100 square root of x plus 4 the whole square plus y square plus z square. Now let us see this is how do we get this inside we put the formula of a minus b the whole square that is equal to a square that is 100 plus b square that is x plus 4 the whole square plus y square plus z square minus 2ab that is minus 2 into 10 into square root of x plus 4 the whole square plus y square plus z square. Now we see that y square plus z square gets cancelled from both the sides. We are left with minus 4 the whole square is equal to 100 plus x plus 4 the whole square minus 20 into square root 4 the whole square plus y square plus z square x plus 16 is equal to 100 plus x square plus 8 x into square root of x plus 4 the whole square plus y square plus z square. In the brackets on both the sides here we applied the formula for a minus b the whole square and here a plus b the whole square we see that x square gets cancelled from both the sides plus 16 gets cancelled from both the sides we have minus 8 x minus 8 x is minus 16 x minus 100 is equal to minus 20 into square root 4 the whole square plus y square plus z square 25 is equal to 4 the whole square plus y square plus z square. Now again squaring both the whole square is equal to 25 into plus y square plus z square it's on both the sides we get 16 x square plus 6 25 is equal to 25 into plus y square plus z square y square minus 25 z 25 is equal to 0. This we get because 16 x square minus 9 8 5 z square we get from the right hand side is equal to 200 x so 200 x minus 200 x becomes equal to 0 25 into 16 is equal to 400 and 6 25 minus 400 is 225. Now this one we get 9 x square plus 25 is equal to 0 so we say that our answer to the question is that the equation of the set of points p the sum of whose distances from the point a that is 400 and the point b that is minus 400 equal to 10 is plus 25 y square 25 z square 5 is equal to 0 so this is our answer to the question I hope that you understood the question and enjoyed the session have a good day