 Hello and welcome to the session. In this session we will discuss a question which says that a point P is rotated such that its distance for a fixed point 2 minus 4 is always equal to 3. Distribute the path fellow by the point P on the coordinate plane. Now let us start with the solution of the given question. Now in the question a fixed point is given to us as 2 minus 4. Now let this fixed point be O having coordinates 2 minus 4 and it is also given that a point P is rotated such that its distance from this fixed point is always equal to 3. Now let this is the point P with coordinates x, y. Now join O with P. Now length of O P gives the distance between the fixed point O and generally point P and we are given that this distance is 3 units. Now to find the path fellow by the point P its distance from this fixed point is always equal to 3. Let us use distance formula. Now if we are given 2 points A and B and coordinates of point A are x1, y1 and coordinates of point B are x2, y2 then according to distance formula the distance AB will be equal to square root of x2 minus x1 whole square plus y2 minus y1 whole square. Now we have to find the distance. Now let coordinates of point O, B and coordinates of point P be x2, y2. So by distance formula distance O P is equal to square root of x1 whole square that is x minus 2 whole square plus y2 whole square. That is y minus minus 4 whole square distance O P is given to us as 3 units. So this is equal to square root of y1 whole square. Now 3 square is 9 and this is equal to x minus 2 whole square plus y plus 4 whole square. Or we can write this equation as x minus 2 whole square plus y plus 4 whole square is equal to 9. Which is the required path at O such that its distance from E equal to 3. We complete this path and it is a circular path with radius O P which is equal to 3 units and radius 3 units which represents the path followed by the point P on the coordinate plane. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.