 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 given by x square plus y square minus a takes plus 10 y minus 12 equal to 0. So let us start with the solution to this question. Now equation of circle given to us is x square plus y square minus a takes plus 10 y minus 12 equal to 0 or we can say x square minus a takes plus y square plus 10 y minus 12 equal to 0. Now completing the squares within the parenthesis what we do now to this bracket we add 16 and to this bracket we add 25 because if we add 16 to this bracket then this becomes x minus 4 the whole square and if we add 25 to this bracket we get y plus 5 the whole square. Since we have added 16 and 25 here so we need to subtract it also so we can say that we have x square minus a takes plus 16 plus y square plus 10 y plus 25 plus minus 12 minus 16 minus 25 equal to 0. This implies x minus 4 the whole square plus y plus 5 the whole square is equal to 53. Now we know that the equation of a circle center is given by h the whole square plus y minus k the whole square equals to r square. Now if we compare this equation to this equation we get to express this as y minus k so we will have y minus of minus 5 and radius r equals to root 53. Therefore our answer to this question is that center is 4 minus 5 and radius is equal to root 53. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.