 Hello and welcome to the session. In this session we discuss the following question that says find the point on y axis which is equally distant from the points 5 minus 2 and minus 3 2. Before we move on to the solution let's recall the distance formula to find the distance between the two given points. Given a point p which coordinates x1, y1 and a point q which coordinates x2, y2, the distance between the points p and q is given by pq which is equal to square root of x2 minus x1 the whole square plus y2 minus y1 the whole square. Or you can say that pq square is equal to x2 minus x1 the whole square plus y2 minus y1 the whole square. This is the key idea that we use for this question. Let's proceed with the solution now. In the question we have that a point on the y axis is equally distant from the given two points. So we suppose let a point p which coordinates 0y be a point on the y axis and we take the other two points as point a which coordinates 5 minus 2 and point b which coordinates minus 3 2. It is given that the point p is equally distant from the point a and point b that is we have pA is equal to pB this means that pA square is equal to pB square. Now using the distance formula let's calculate what is pA square this is equal to 5 minus 0 the whole square plus minus 2 minus y the whole square that is we have pA square is equal to 5 square plus 2 plus y the whole square. Further pA square is equal to 25 plus 4 y plus y square or you can say that pA square is equal to y square plus 4 y plus 29. So we have got the value for pA square. Now let's find out the value for pB square this is equal to minus 3 minus 0 the whole square plus 2 minus y the whole square this gives us pB square is equal to minus 3d whole square plus 2 minus y the whole square which gives us pB square is equal to 9 plus 4 minus 4 y plus y square this gives us pB square is equal to y square minus 4 y plus 13. So we have got the value for pB square also. Now since we have pA square is equal to pB square so this means that y square plus 4 y plus 29 is equal to y square minus 4 y plus 13. Now y square cancels with y square and this further gives us 4 y plus 29 plus 4 y is equal to 13 further 8 y is equal to 13 minus 29 this gives us 8 y is equal to minus 16 so we get y is equal to minus 2. Now that we have got the y is minus 2 so the point on the y axis which is given by p which coordinates 0 y is the point p which coordinates 0 minus 2. So p which coordinates 0 minus 2 is the required point. This completes the session hope you have understood the solution of this question.