 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 circle with radius 5 whose center lies on x axis and passes through the point 2, 3. So let us start with the solution to this question. We already know that equation of the circle with center some point h k and radius r is given by x minus h the whole square plus y minus k the whole square equals to r square and we call this equation 1 or we may call this equation A as in the question that the center lies on x axis and passes through the point 2, 3. So what we do is we put the point x y equation A the whole square equals to r square plus h square minus 4 h plus 9 plus k square h minus 613 equals to r square and we call this equation 1. Now it is given that center lies on x axis thus value of coordinate on the y axis equal to 0 r is given to be 5. So we can say that r square is equal to 25 which in 1 we get so this is equal to 25 or we can say this is h square minus 4 h minus 12 equal to 0. Now splitting the middle term 6h minus 12 equal to 0. Now from the first two terms we take h common and we have h plus 2 now from x common and in the bracket we have h plus 2 equal to 0. So this becomes h minus 6 equal to 0 and this gives us or h equal to minus 2 because if we put separate bracket equal to 0 we get h equal to 6 or minus 2. So we have two equations of the circle. First of all we put point h k radius r equal to 5 in equation A that is x minus h the whole square plus y minus k the whole square equal to r square we get 6 the whole square plus y minus 0 the whole square is equal to 25 or this can be further written as 6 minus 12x plus y square minus 25 is equal to 0. This simplifies further to x square plus y square minus 12x plus 11 equal to 0 this is one of the equations. Next we put the point h k as minus 2 0 now because we had h equal to 6 and minus 2 and k was 0 and r equal to 5 again in equation A we get x minus of minus 2 the whole square plus y minus 0 the whole square equal to 25 that is r square this is x plus 2 the whole square plus y square equal to 25 or plus 4x plus y square minus 25 equal to 0 and further simplifying this we get x square plus y square plus 4x minus 21 equal to 0 this is the second equation. So our answer to the question is the two equations of the circle with the radius 5 who centralize on x axis and passes through the point 2 3 is x square plus y square plus 4x minus 21 equal to 0 plus y square minus 12x plus 11 equal to 0. So the required equation will be any one of these two equations. So I hope that you understood the question and enjoyed the session have a good day.