 Hello friends, welcome to the session ahamalka. Let's discuss the given question. Find the center of the circle passing through the points 6 minus 6, 3 minus 7 and 3, 3. Now let's begin with the solution. According to the question we have to find the center of the circle. So let P be the center of the circle with x, y coordinates and the circle passes through the point A, B and C. Let P be the center of circle with coordinates x and y. We all know that the all the radii of the circle are equal. Therefore, we can say that AP equal to PB equal to PC. Now or we can say AP square equal to VP square equal to PC square. Now to find AP, VP, PC we'll apply the distance formula and we know the distance formula is that is to find the distance between the two points A and B with coordinates of A as x1, y1 and that of V as x2, y2. The distance between them is given by AB equal to square root of x1 minus x2 square plus y1 minus y2 square. So this is the distance formula. Now we are going to use it to find AP, VP and PC. Now apply distance formula to find AP square, PB square and PC square. So apply distance formula we get AP square equal to x minus 6 square plus y minus 6 that will be y plus 6 square that is AP square. Now we'll find PB square which is equal to x minus 3 square plus y minus 7 that will be y plus 7 square equal to PC square which is equal given by minus 3 square plus y minus 3 square. Now on equating x minus 6 square plus y plus 6 square with x minus 3 square plus y plus 7 square we get this implies x square plus 36 minus 12x plus y square plus 36 plus 12y equal to x square minus 6x plus 9 plus y square plus 14y plus 49. So this implies now on simplification we get minus 6x minus minus 2y equal to minus 14 or we can say taking minus 2 common we get 3x plus y equal to 7 and this we are first equation. Now again on equating x minus 3 square plus y plus 7 square with x minus 3 whole square plus y minus 3 whole square we get minus 3 square plus y plus 7 square with x minus 3 square plus y minus 3 square. So this implies now we'll open the bracket and we get x square plus 9 minus 6x plus y square plus 49 plus 14y equal to x square plus 9 minus 6x plus y square plus 9 minus 6y. This implies on simplification we get 20y equal to minus 40. Therefore we can say that y equal to minus 2 substituting value of y equal to minus 2 in equation first we get our first equation is 3x plus y equal to 7. Now we'll substitute y with minus 2 we get 3x minus 2 equal to 7 or we can say 3x equal to 9 or x equal to 3. Therefore x equal to 3 and y equal to minus 2. Now since we have to find the coordinates of the point P that is the center of the circle which are given by x and y and x is equal to 3 and y is minus 2. Therefore we can say therefore center of circle is 3 minus 2. So hope you understood the solution and enjoyed the session. Goodbye and take care.