 Hi, and welcome to our session. Let us discuss a problem question. The question says the perpendicular from the origin to the line y is equal to mx plus c meets at the point minus y2. Find the value of m and c. Let's now begin with the solution. Let a be the line whose equation is y is equal to mx plus c. The perpendicular is drawn from the origin on this line. And this line meets a be at n whose coordinates are minus 1, 2. We have to find the value of m and c. Now, equation of line av is y is equal to mx plus c. Now, we will find the slope of line om. We know that slope of line passing through points x1, y1, and x2, y2 is y2 minus y1 upon x2 minus x1. So slope of line passing through 0, 0 minus 1, 2 is 2 minus 0 upon minus 1 minus 0. And this is equal to minus 2. Now, since om is perpendicular to ab, therefore slope of om into slope of ab is equal to minus 1. Now, slope of om is minus 2. So we have minus 2 into slope of ab is equal to minus 1. Now, this implies slope of ab is equal to 1 by 2. Now, this ab passes through the point minus 1, 2. And we know that equation of line passing through point x1, y1, and having slope m is pi minus y1 is equal to m into x minus x1. Now, here slope is 1 by 2, and x1, y1 is minus 1, 2. So equation of line ab which passes through minus 1, 2 and has slope 1 by 2 is y minus 2 is equal to 1 by 2 into x plus y. Now, this implies y minus 4 is equal to x plus 1. This implies 2y is equal to x plus pi. And this implies y is equal to 1 by 2 into x plus pi by 2. Now, this equation is of the form y is equal to mx plus c. On comparing this equation that y is equal to mx plus c, we find that m is equal to 1 by 2 and c is equal to pi by 2. Hence, our required value of m is 1 by 2 and c is pi by 2. This is our required answer. So this couple is the session I and take care of.