 Hello and welcome to the session. In this session we will discuss a question which says that find the length of the part intercepted by the circle x square plus y square is equal to 25 on the line 2x minus y plus 5 is equal to 0. Now before starting the solution of this question we should know some results. Now the standard form of the equation of circle h whole square plus y minus k whole square is equal to r square where the variance of center k and variance of the circle is r. y plus b y plus c is equal to 0 and the point p x1 y1 the distance of point p from the given line that is this line is given by mod of a x1 plus b y1 plus c whole upon square root of a square plus b square. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now the equation of the circle is given to us So given the equation of the circle is x square plus y square is equal to 25 and let us name this as 1. Now this is the standard form of the equation of circle in which the coordinates of center are hk. Now comparing this equation with the standard form of the equation of circle here coordinates of center c of the circle which is given by equation number 1 r00. Now also in this equation r represents the variance of the circle. Now form 1 we have this y square is equal to 25 which implies x square plus y square is equal to 5 square. Therefore radius which is given by equation number 1 is the equation of the line is given to us also given the equation of minus y plus 5 is equal to 0. Now this is the circle with center c00 and this is the line minus y plus 5 is equal to 0 which is intersecting this circle. Now let us take these points where the line is intersecting the circle as a is perpendicular y plus 5 is equal to 0 from the 0 0 which is cd where we use this formula. cd will be equal to mod of a x1 plus by 1 plus c whole upon square root of a square plus b square where this line represents a x plus by plus c is equal to 0 is equal to mod of 2 into 0 minus 0 plus 5 square root of a square which is 2 square plus b square which is minus 1 square which is equal to mod of 5 over square root of 4 plus 1 which further gives cd is equal to root 5 units. Now in a right angle triangle c square is equal to ad square plus cd square this is the radius which is equal to 5 cd is equal to root 5 all these values here this implies 5 square is equal to ad square plus root 5 ad square is equal to 25 is equal to 22 square root of 20 which is equal to 2 root 5 this implies ad is equal to 2 root 5 units equal to ad from the center of the circle ad is equal to db also ad can be written as ad plus db further this implies ad is equal to ad plus db is equal to ad so here db can be replaced by ad which further implies ad is equal to 2 into ad now we have ad is equal to 2 root 5 units value here ad is equal to 3 into 3 root 5 which is equal to 4 root 5 units wide length ad is equal to 4 root 5 units enough for a given question and that's all I have enjoyed the session