 Hi and welcome to the session. Let us discuss the following question. The question says, show that the equation of the line passing through the origin and making an angle theta with the line y is equal to mx plus c is y by x is equal to plus minus n plus tan theta upon 1 minus m tan theta. This is the line o p which is passing through the origin and this is the line p q whose equation is y is equal to mx plus c. And this line p o makes angle theta with p q. We have to show that equation of line p o is pi by x is equal to plus minus m plus tan theta upon 1 minus m tan theta. Let us now begin with the solution. Let p q be a line whose equation is y is equal to mx plus c. Now let slope of line p o is m 1. Line p o makes angle theta with line p q therefore tan theta is equal to plus minus m1 minus m upon 1 plus m1 into m. Because we know that angle between two lines having slope m1 and m2 is given by tan theta is equal to mod of m2 minus m1 upon 1 plus m1 into m2. Now first consider tan theta is equal to m1 minus m upon 1 plus m1 into m. Now this implies tan theta plus m1 m tan theta is equal to m1 minus m. This implies m1 into 1 minus m tan theta is equal to m plus tan theta. This implies m1 is equal to m plus tan theta upon 1 minus m tan theta. Let us name this equation as equation number 1. Now consider the negative sign. So now we have tan theta is equal to minus m1 minus m upon 1 plus m1 into m. Now this implies tan theta plus m1 m into tan theta is equal to minus m1 plus m. This implies m1 into 1 plus m tan theta is equal to m minus tan theta and this implies m1 is equal to m minus tan theta upon 1 plus m tan theta. Let us name this equation as equation number 2. Now equation of line OP which is passing through the origin and having slope m1 is y is equal to m1 x. Now y is equal to m1 into x implies y by x is equal to m1 from 1. We know that m1 is equal to m plus tan theta upon 1 minus m tan theta and from 2 we know that m1 is equal to m minus tan theta upon 1 plus m tan theta. Hence we have proved that equation of line through the origin and making an angle theta with the line y is equal to mx plus c is y by h is equal to m plus minus tan theta upon 1 plus minus m tan theta. This is our required answer. Bye and take care.