 Hello and welcome to the session. In this session we will discuss a question which says that final equations of the bisectives of the angle between the straight lines 3x plus 4y plus 2 is equal to 0 and 5x minus 12y minus 6 is equal to 0. Now before starting the solution of this question we should know how to solve it and that is from the lines L1 and L2 where L1 is given by A1x plus B1y plus C1 is equal to 0 and L2 is given by A2x plus B2y plus C2 is equal to 0 the equations of the bisectives of the angles between the lines L1 and L2 are given by plus B1y plus C1 whole upon square root of plus B1 square is equal to plus minus plus B2y plus C2 whole upon square root of plus B2 square. The equation obtained on taking the positive sign will be the equation of the bisector, the originalisative sign will have the equation of the other bisector. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Now in the equation the equations of the lines are given to us. So given the equations of the lines plus 4y plus 2 is equal to 0 and 5x minus 12y minus 6 is equal to 0. Now writing the given equations the constant terms are positive plus 4y is equal to 0 and minus 5x plus 12y plus 6 is equal to 0. Now here we are getting both the constant terms that are 2 and 6 as positive. Now let us name this as 1 and this as 2. Now to find the equations of the bisectives of the angle between the lines 1 and 2 where we use this formula. Now the equations of the angle bisectives of 1 and 2 is given by plus 4y plus 2 whole upon square root of 3 square plus 4 square is equal to plus minus minus 5x plus 12y plus 6 whole upon square root of minus 5 square plus 12 square plus b1y plus c where a1 is 3 and b1 is 4 over square root of a1 square plus b1 square plus b2y plus c2 over square root of b2 square where a2 is equal to minus 5 and b2 is equal to 12 plus 4y plus 2 whole root of 3 square is 9 plus 4 square is 16 is equal to plus minus minus 5x plus 12y whole upon square root of minus 5 square is 25 plus 12 square is 144 4y plus 2 whole upon square root of 25 minus 5x plus 12y whole upon square root of 25 plus 144 is 169 which further implies 3x plus 4y plus 2 is equal to plus minus minus 5x plus 12y whole upon square root of 169 is 13. This equation by taking the real equation of the bisector, the bisector now in this equation taking the positive sign it will be 3x plus 4y plus 2 equal to plus 12y plus 6 on truss multiplying 13 into 3x plus 4y plus 2 whole is equal to 5 into minus 5x plus 12y plus 6 the whole. This implies 12y plus 26 is equal to minus 25x plus 16y plus 30. 12y minus 16y plus 26 minus 30 is equal to 0. This we get 60y is minus 8y and here 26 minus 30 is minus 4 is equal to 0. Now this implies taking 4 common within brackets it will be 16x minus 2y minus 1 is equal to 0 which further implies 16x minus 2y minus 1 is equal to 0. So this is the equation of the bisector of the angle in which the origin lies. Now by taking the negative sign the equation of the other bisector can be obtained. Now in this equation the negative sign the equation plus 4y plus 2 whole upon is equal to minus 12y plus 13 which implies 3x plus 4y plus 2 whole upon 5 is equal to 5x minus 12y minus 6 whole upon 13. Now on truss multiplying this implies 13 into 3x plus 4y plus 2 whole is equal to 5 into 5x minus 12y minus 6 the whole. Which further implies plus 26 is equal to 25. Other implies 39x minus 25x plus 52y plus 30 is equal to 0. Further implies 40x plus 112y plus 56 is equal to 0. Further on taking 14 common within brackets it will be x plus x plus 8y plus 4 is equal to 0. Therefore equation of the other bisector the equation of the bisector minus 1 is equal to 0 the equation of the other bisector is the solution of the given question and that is all for this session.