 Hello and welcome to the session. In this session we will discuss a question which says that a straight line L is perpendicular to the line 5x-y is equal to 1. The a on the triangle formed by the line L and coordinate axis is 5. Find the equation of flying. Now before starting the solution of this question, we should know some results. And first is the equation ay-bx plus k is equal to 0 represents for different values of k 3 of lines perpendicular plus by plus c is equal to 0. That means that if we want to find the equation of any line perpendicular to this line, then integrate the coefficient of x and y and change the sign of ay-bx or y and replace the constant term by a new constant k. That is the other a-b-c if the coordinates of y are coordinates of b are x2, y2, x3, y3, then any of the triangle a-b-c into x1, y2 minus x1, y3 plus x2, y3, x2, y1 plus x3, y2. The whole. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. We will find the equation of straight line L which is perpendicular to this line. The equation of line is 5x minus y is equal to 1 and the written as 5x minus y minus 1 is equal to 0. Now by using this result which is given as a key idea, the equation of any line a plus 5y minus k is equal to 0. Now let us move this as, now for rather this equation, in equation number 1 we have introduced the coefficients of x and y and change the sign of y and also replace the constant with a new constant k. Now in which is given by equation number 2, xx is equal to 0 into vx 5 into 0 minus k is equal to 0 which implies x minus k is equal to 0 which further implies x is equal to k. Therefore coordinates, now again if the line which is given by equation number 2 point b then 4v 0 plus 5y minus k is equal to 0 which further gives 5y is equal to k and this implies y is equal to k by 5. Therefore coordinate point b, now let this be the line L which cuts the x axis at the point a whose coordinates are k0 and cuts the y axis at the point b whose coordinates are 0 k by 5 and o which is the origin and its coordinates are 0 0. Now in the found between the line L and the coordinate axis is the triangle aob. Now in the equation the area of this triangle is given as following this formula, the coordinates of a as x1 y1, coordinates of p as x2 y2 and coordinates of o as x3 y3. Now using the formula area of triangle aob will be equal to 1 by 2 into x1 y2 minus x1 y3 plus x2 y3 minus x2 y1 plus x3 y1 minus x3 y2. Now putting the value of x1 y1, x2 y2 and x3 y3 here this will be equal to 1 by 2 into k into k by 5 minus 0 plus 0 minus 0 plus 0 minus 0 the whole except the first term will become 0 which is equal to 1 by 2 into k square by 5. Therefore is equal to k square by 10 which further implies 50 is equal to k square which further gives k square is equal to 50 and this implies the equation of the line L which is the equation number 2. Now putting equal to plus 5 root 2 in equation number 2 we get 5 y minus or plus 5 root 2 is equal to 0 which implies this 5 root 2 is equal to 0. Now putting 5 root 2 in equation number 2 we get 5 y minus or minus 5 root 2 is equal to 0 which implies x plus 5 y plus 5 root 2 is equal to 0. Now for the true value of k we are getting two equations of the line L. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.