 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says, find the equation of the circle with center 1 by 2, 1 by 4 and radius 1 by 12. So let us start with the solution to this question. Here we are given center that is hk is equal to 1 by 2, 1 by 4 and radius r is equal to 1 by 12. Now we know that equation for circle is given by minus h the whole square plus y minus k the whole square is equal to r square. So now we simply put in the values of hk and r as 1 by 2, 1 by 4 and 1 by 12 in this equation and we get x minus 1 by 2 the whole square plus y minus 1 by 4 the whole square is equal to 1 by 12 the whole square. Now on opening the brackets on the left hand side we get x square plus 1 by 4 minus x plus y square plus 1 by 16 minus 1 by 2 y is equal to 1 by 144 because square of 12 is 144. Now this implies that x square plus y square minus x minus 1 by 2 y plus now we take constants in one bracket and we get 1 by 4 plus 1 by 16 minus 1 by 144 is equal to 0. Now this implies x square plus y square minus x minus 1 by 2 y plus now we solve this here first of all we take the LCM of denominators of the three terms that is 144 in the numerator we will have 36 plus 9 minus 1 equal to 0. This implies that x square plus y square minus x minus 1 by 2 y plus now 36 plus 9 minus 1 44 divided by 144 is equal to 0. This implies x square plus y square minus x minus 1 by 2 y. Now on cancelling this we get 11 divided by 36 because we have divided the numerator and denominator by 4 so we get 11 by 36 equal to 0 by 36 we get 36 x square plus 36 y square minus 36 x 11 equals to 0. So we say that our answer to this question is that the equation of the circle with center 1 by 2 1 by 4 and radius 1 by 12 is 36 x square plus 36 y square minus 36 x minus 18 y plus 11 equals to 0. So this is our answer to the question I hope that you understood the question and enjoyed the session have a good day.