 Hello and welcome to the session. Let us discuss the following question that says, find equation of the line through the 0.02 making an angle 2 pi upon 3 with the positive x axis also find the equation of line parallel to it and crossing the y axis at a distance of 2 units below the origin. So first let us learn the equation of a line passing through a given point suppose the given point is x1, y1 having slope m is given by y minus y1 is equal to m times of x minus x1 where x, y is any general point on the line. So with the help of this idea we are going to solve the above problem. So this is our key idea. Let us now start with the solution. Now here we are given the point 0.02 through which the line passes and also we are given that the line makes an angle of 2 pi upon 3 with the positive x axis. So the slope tan theta where theta is 2 pi upon 3 which is the angle made by the line with the positive x axis so we have tan 2 pi upon 3. Let us denote the slope by m. Now tan 2 pi upon 3 is tan pi minus pi upon 3 which is equal to tan pi upon 3 with a negative sign which is further equal to tan pi upon 3 is root 3 with a negative sign. Therefore slope m is equal to minus root 3. Now by a key idea we know that equation of a line passing through the point 0.02 with slope minus root 3 is given by y minus 2 is equal to minus root 3 into x minus 0. That is root 3 x plus y minus 2 is equal to 0. So this is the required equation of a line. Let this be equation number 1. Now the question further says also find the equation of a line parallel to it and crossing the y axis at a distance of 2 units below the origin. So 2 units below the origin is this point and it is denoted by 0 minus 2. So we have to find the equation of a line which passes through a point 0 minus 2 and its slope is equal to the slope of the line which passes through the point 0.02 and makes an angle of 2 pi upon 3 and therefore we can say that equation of the line passing through the point 0 minus 2 having slope minus root 3 which is the slope of the given line which passes through 0 to parallel to line 1 is given by y minus of minus 2 is equal to slope which is minus root 3 into x minus 0. So further that y plus 2 is equal to minus root 3 into x or root 3 x plus y plus 2 is equal to 0. So this is the second equation of the required line. Hence our answer is equation of the line which passes through the point 0 to and making an angle 2 pi upon 3 with the positive x axis is root 3 x plus y minus 2 is equal to 0 and the equation of the line parallel to this line and crossing the y axis at a distance of 2 units below the origin is root over 3 into x plus y plus 2 is equal to 0. So this concludes the session. Hope you have understood it very well. Take care and have a good day.