 Hello and welcome to the session. In exercise 1-8, find the equation of the line which satisfy the given conditions. 8th one is perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x axis is 30 degrees. First, let us learn the equation of the line normal distance p on the origin angle omega which the normal makes with the positive direction of x axis is given by cos omega plus y sin omega is equal to p. 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 and here we are given at the perpendicular distance from the origin is 5 units. So, this implies p which is the normal distance is equal to 5 units and angle made by the perpendicular with the positive x axis is 30 degrees. So, omega is equal to 30 degrees. So, by a key idea equation of line is given by 30 degrees plus y sin 30 degrees is equal to p that is 5 or we have x cos 30 degrees is root 3 upon 2 plus y sin 30 degrees is half is equal to 5 or we have root 3 into x plus y is equal to 10. Thus equation of a line which satisfies the given condition is given by root 3 into x plus y is equal to 10. So, this is our answer. Hope you have understood it. Take care and have a good day.