 Hello and welcome to the session. In this session, we will discuss the question which says that the x coordinate of a point p is twice its y coordinate. If p is equidistant from q to minus 5 and r minus 3 6, then find the coordinates of p. Now before starting the solution of this question, we should know a result. And that is if the coordinates of point a are x1, y1 and the coordinates of point b are x2, y2, then by distance formula, distance a b is equal to square root of x1 minus x2 whole square plus y1 minus y2 whole square. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Now in the question it is given that the x coordinate of a point p is twice its y coordinate. Now let the y coordinate of p is y. It is given that the x coordinate of a point p is twice its y coordinate will be 2y, point p r and y. It is given that the point p is equidistant from the point q and r whose coordinates are given to us. Now given the point p is equidistant from the point q whose coordinates are 2 minus 5 and the point r whose coordinates are minus 3 6. Now since p is equidistant from the point q and r, therefore distance pq will be equal to distance pr. Out the distance pq and pr when we use the distance formula which is given in the key idea. So this implies now the coordinates of p are 2y and y and the coordinates of q are 2 minus 5. So the distance pq will be square root of minus 2y whole square plus minus 5 minus y whole square. Which is equal to distance pr and here the coordinates of p are also given to us and the coordinates of r are also given to us. So the distance pr will be equal to square root of minus 3 minus 2y whole square plus 6 minus y whole square. Now square root both sides is 2y whole square 5 minus 5 whole square is equal to minus 3 minus 2y whole square plus this formula implies y square minus 8y plus y square plus 10y plus 4y square plus 12y plus 36 plus y square minus 12y. Now this implies plus 4y square minus 8y plus 25 plus y square plus 10y minus 9 minus 4y square minus 12y minus 36 minus y square plus 12y is equal to 0. Now this implies answer with each other is 29 plus 10y is plus 2y minus 9 minus 36 is minus 45 is equal to 0 is equal to 0. 16 which further gives i is equal to 692 which is equal to 8 2y. Now we have the y coordinate of p as 8 p will be equal to 2y which is equal to 2 into 8 which is equal to 16. Therefore x is equal to 16. Hence the question and answer for this session hope you all have enjoyed the session.