 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 center and radius of the circle x square plus y square minus 4x minus 8y minus 45 equals to 0. So let us see the solution to this one. Now equation of the circle given to us is x square plus y square minus 4x minus 8y minus 45 equal to 0 or we can say that x square minus 4x plus y square minus 8y minus 45 is equal to 0. Now completing the squares within the parenthesis we can write x square minus 4x plus 4 plus y square minus 8y plus 16. Now we add 4 because we know that on adding 4 we will get this as x minus 2 the whole square and we have added 16 because we know that on adding 16 this becomes y minus 4 the whole square. Since we have added 4 and 16 so we need to subtract also so we will have plus minus 45 minus 4 minus 16 equal to 0. Now this implies that x minus 2 the whole square plus y minus 4 the whole square is equal to 65. Now we know that equation of circle with center radius r is given by x minus h the whole square plus y minus k the whole square equals to r square. Now on comparing these two we can say that the point hk is same as 2 4 and the radius r will be equal to under the root 65. So our answer to this question is center is 2 4 and radius is equal to root 65. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.