 Hello and welcome to the session. In this session we will discuss a question which says that find the points on which the line x plus 2y is equal to 11 cuts the circle x2 plus y2 plus 2x minus 2y minus 23 is equal to 0. Now we will start with the solution. Now the equation of the line is given to us. So given the equation of the line is x plus 2y is equal to 11 which implies x is equal to 11 minus 2y. Now let us name this as 1 also the equation of the circle is given to us. So given the equation of the circle 2 plus y2 plus 2x minus 2y minus 23 is equal to 0. Now let us name this as equation number 2. Now putting whole square plus y2 plus 2 into 11 minus 2y the whole minus 23 is equal to 0. Plus 4y square minus 44y plus y square plus 22 minus 4y minus 2y minus 23 is equal to 0. Minus 52y plus 120 is equal to 0. Now taking 5 common it will be 5 into y square minus 10y plus 24 the whole implies y square minus 10y plus 24 is equal to 0. Now this is the quadratic equation in y this implies y square minus 6y minus 4y plus 24 is equal to 0. Which further implies I am taking y common it will be y into y minus 6 the whole and from these two terms taking minus 4 common it will be minus 4 into y minus 6 the whole is equal to 0. Which further implies y minus 6 the whole into y minus 4 the whole is equal to 0. Now this implies either whole is equal to 0 which further implies y is equal to 6 or y is equal to 4. Now this is the equation number 1 so putting y is in equation number 1 we get is equal to 11 minus 2 into 6 which is equal to 11 minus 12 which is equal to minus 1. Now putting y is in equation 1 again we get equal to 11 minus 2 into 4 equal to 11 minus 8 which is equal to 4 then equal to 3 y is equal to 6 then x is equal to minus 1. Therefore the required points the line that is this the given line the given circle the solution of the given question and that's all for this session hope you all have enjoyed the session.