 Hello and welcome to the session. In this session we will discuss a question which says that if the straight line 3x plus 4y is equal to 25, that is the circle, x square plus y square is equal to a square, find the radius of the circle. Now we will start with the solution. Here the equation of the straight line is given to us and the equation of the circle is also given to us. So given equation of the straight line is 3x plus 4y is equal to 25, let us name it as 1 and equation of the circle is x square plus y square is equal to a square and let us name this as 2. From 1 we have 3x plus 4y is equal to 25 which implies 4y is equal to 25 minus 3x which further gives y is equal to 25 minus 3x whole upon 4. Now substituting y is equal to 25 minus 3x whole upon 4 in equation number 2 which is this equation we get x square plus 25 minus 3x whole upon 4 whole square is equal to a square which further implies x square plus 625 minus 150x plus 9x square whole upon 16 is equal to a square. Now on taking the LCM this implies 16x square plus 625 minus 150x plus 9x square whole upon 16 is equal to a square which further implies x square plus 9x square is 25x square plus 625 minus 150x is equal to 16a square. Now this implies 25x square minus 150x plus 625 minus 16a square is equal to 0. Now let us name this equation as equation number 3. Now we have a result according to which if the line 1 which is this line touches the circle which is given as equation number 2 then the roots of this quadratic equation are equal. So we can write given by equation number 1 touches the circle given by equation number 2 then the roots of the quadratic equation which is given by 3 are equal. Now which are equal then minus 4ac which is the discriminant is equal to 0. Now for this equation here a is equal to 25, b is equal to minus 150 and c is equal to 625 minus 16a square. So substituting the values of a, b and c here this implies minus 150 whole square minus 4 into 25 into 25 minus 16a square the whole is equal to 0. Now this can also be written as minus 150 whole square is equal to 4 into 25 into 625 minus 16a square the whole which further implies minus 150 whole square is 22,500 is equal to 4 into 25 which is 100 into 625 minus 16a square the whole. Further this implies 225 is equal to 625 minus 16a square which further implies 16a square is equal to 625 minus 225 which implies 16a square is equal to 400 this implies a square is equal to 400 by 16 which further implies square is equal to here 4 into 100 is 400 and 4 into 4 is 16 further 4 into 25 is 100 so it will be 25 this further implies a is equal to 5. Now we know that if the equation of the circle is a plus y square is equal to a square then a represents the radius of circle hence the radius of the circle which is a is equal to five units so this is the solution of the given question and that's all for the session hope you all have enjoyed the session