 Hello and welcome to the session. Let's work out the following problem. It says what point on the x-axis is equidistant from the points 7, 6 and minus 3, 4. So we have to find a point on the x-axis which is equidistant from the point 7, 6 and minus 3, 4. So let's now move on to the solution and let the point on the x-axis be p x 0. Since the point lies on x-axis, y coordinate must be 0 and we are given that p x 0 is equidistant from the points a 7, 6, let's name this point as a and b minus 3, 4. Now distance between the points p x 1, y 1 and q x 2, y 2 is given by the formula under the root x 2 minus x 1 whole square plus y 2 minus y 1 whole square. So this is the distance between the points p q, right? You must remember this formula. Now we are given that distance between p x 0 and a is same as distance between p x 0 and the point p. So we have p a is equal to p b. Now the distance between p a will be 7 minus under the root 7 minus x whole square plus 6 minus 0 whole square is equal to the distance between p and b. Distance between p and b will be given by minus 3 minus x whole square plus 4 minus 0 whole square. Now taking square on both sides we have 7 minus x whole square plus 6 minus 0 whole square is equal to minus 3 minus x whole square plus 4 minus 0 whole square. Now again it is 7 minus x whole square plus 6 square taking minus 1 common and since it's square it will become positive. So we have 3 plus x whole square plus 4 square. Again this is equal to now using the formula of a minus b whole square we have 7 square that is 49 plus x square minus 2 into 7 into x that is minus 14 x plus 36 is equal to now here we will use the formula of a plus b whole square. So we have 3 square that is 9 plus x square plus 2 into 3 into x that is 6x plus 16. Again x square gets cancelled on both sides we have 49 plus 36 is 85 minus 14x is equal to 9 plus 16 is 25 plus 6x. So this implies 85 minus 25 is equal to 6x plus 14x. So this implies 60 is equal to 6x plus 14x that is 20x. So this implies x is equal to 60 upon 20. So this implies x is equal to 3. Therefore the required point on xx is which is equal distance from the point 7, 6 and minus 3, 4 is 3, 0. So this completes the question and the session. Bye for now. Take care and have a good day.