 Hello and welcome to the session. In this session we will discuss a question which says that find the equation of the circle passing through the points of intersection of the circles x plus 3 volt square plus y plus 3 volt square is equal to 9 and x minus 1 volt square plus y minus 1 volt square is equal to 4 and has its center on y axis. Now before starting the solution of this question we should know some results. First is let s1 is equal to 0 and s2 is equal to 0 be the two equations of circle where s1 is x square plus y square plus 2g1x plus 2f1y plus c1 plus y square plus 2g2x plus 2f2y plus c2 then s1 plus k into s2 is equal to 0 where k is not equal to minus 1 represents two of circles the points of intersection of the given circles. Now the general equation of the circle x square plus y square plus 2gx plus 2f1y plus c is equal to 0 where the coordinates of the center are given by minus g minus f. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now here the equations of the circles are given to us. So given the equation of the first circle is 2 volt square plus y plus 3 volt square is equal to 9. This implies plus 4 plus 4x plus y square plus 9 plus 6y is equal to 9 which further implies x square plus y square plus 4x plus 6y plus 4 plus 9 minus 9 is equal to 0 which implies x square plus y square plus 4x plus 6y plus 4 and these terms are cancelled with each other so this is equal to 0. Now let us name this as equation number 1. Also given the equation in circle minus 1 volt square plus y minus 1 volt square is equal to 4. This implies x square plus 1 minus 2x plus y square plus 1 minus 2y is equal to 4 which further implies x square plus y square minus 2x minus 2y plus 1 plus 1 minus 4 is equal to 0 which further implies x square plus y square minus 2x minus 2y minus 2 is equal to 0. Name this as equation number 2. Now by using this result which is given in the key idea for the equation 1 and equation 2 the family of circles required is x square plus y square plus 4x plus 6y plus 4 plus k into x square plus y square minus 2x minus 2y minus 2 the whole is equal to 0. Here as s1 is equal to 0 is equal to 0. s1 plus k into s2 is equal to 0 represents a family of circles passing through the points of intersection of the given circles. Further this implies x square plus y square plus 4x plus 6y plus 4 plus kx square plus ky square minus 2kx minus 2k is equal to 0 which further implies 1 plus k the whole into x square plus 1 plus k the whole into y square plus whole into x plus 6 minus 2k the whole into y plus to 0. Now dividing throughout by k plus 1 this implies whole upon k plus 1 the whole into x plus 6 minus 2k whole upon k plus 1 the whole into y. This implies x square plus y square plus k plus 1 into x the whole whole upon k plus 1 into y plus whole upon k plus 1 the whole is equal to 0. Now this is the general equation of the circle and this is n minus f. So here n is k the whole whole upon k plus 1 and minus therefore center a whole upon k plus 1 minus 3 whole upon k plus 1 in the equation of the circle which has its center and y axis. For the member circle center that means the x coordinate of it will be k minus 2 whole upon k plus 1 is equal to 0 which further gives k is equal to 2. So this equation as equation number 3 number 3 y plus 4 to the whole is equal to minus 4x minus 4y minus 4 now here each other. So this is the required equation solution of the given question and that's all for the session hope you all have enjoyed the session.