 Hello and welcome to the session. Let us discuss the following question. It says, find the values of theta and p if the equation x cos theta plus y sin theta is equal to p is the normal form of the line root 3x plus y plus 2 is equal to 0. Now, to find the values of theta and p will first convert the general form of line in the normal form and then compare that normal form with this. So, if we are given the general form or general equation of a line given by ax plus by plus c is equal to 0 then the normal form is given by minus a upon under root of a square plus b square x minus b upon under root of a square plus b square y is equal to c upon under root of a square plus b square. So, this knowledge will work as k idea. Let us now proceed on with the solution. The general equation of line is given to be root 3x plus y plus 2 is equal to 0. We now convert this into a normal form for that we need to obtain the root of square of coefficient of x plus square of coefficient of y which is given by under root of root 3 square plus 1 square this is equal to root 4 which is equal to 2. Now, the normal form is this. So, the normal form is minus a upon under root of a square plus b square here a is root 3 and under root of a square plus b square is 2x minus b upon under root of a square plus b square here b is 1 and it is minus 1 upon 2y is equal to c upon under root of a square plus b square here c is 2. So, this is equal to 2 upon 2. So, this is equal to minus root 3 by 2x minus 1 by 2y is equal to 1. Now, we know that the normal form of the line is x cos theta plus y sin theta is equal to p. Now, comparing 1 and 2 we get cos theta is equal to minus root 3 by 2 and sin theta is equal to minus 1 by 2 and p is equal to 1. Now, we use any one of these two equations to find the value of theta we use cos theta is equal to minus root 3 by 2. We know that cos pi by 6 is root 3 by 2. So, cos theta is equal to cos pi plus pi by 6 since we have cos theta is equal to minus root 3 by 2 that is cos theta is equal to cos 7 pi by 6. So, this implies theta is equal to 7 pi by 6 and we have obtained p as 1. Hence, theta is 7 pi by 6 and p is 1. So, that is all for this session. Goodbye and take care.