 Hi, and welcome to our session. Let us just ask the following question. The question says, reduce the following equations into normal form. Find the perpendicular distances from the origin and angle between perpendicular and the positive x-axis. First part is x minus root 3 by plus 8 is equal to 0. Now before solving this question, we should know that normal form of the equation ax plus vy plus c is equal to 0 is x cos omega plus y sine omega is equal to p, where p is the perpendicular distance from origin. Omega is the angle made by a perpendicular with x-axis. So always remember that normal form of the equation ax plus vy plus c is equal to 0 is x cos omega plus y sine omega is equal to p, where p is the perpendicular distance from origin, and omega is the angle made by a perpendicular with x-axis. Let's now begin with the solution. Given equation is x minus root 3y plus 8 is equal to 0. We will first reduce this equation into normal form. Let's first shift the constant to the right-hand side. So we have x minus root 3y is equal to minus 8. Now we will make this constant to be positive by multiplying both sides by minus 1. So by multiplying both sides by minus 1, we get minus x plus root 3y is equal to 8. Now we will divide both sides by square root of coefficient of x whole square. Now here coefficient of x is minus 1. So we have minus 1 square plus coefficient of y whole square. Now here coefficient of y is root 3. So we have root 3 square. And this is equal to 2. So by dividing this equation on both sides by 2, we get minus 1 by 2 into x plus root 3 by 2 into y is equal to 4. Now minus 1 by 2 is equal to cos 120 degree. And root 3 by 2 is equal to sine 120 degree. So minus 1 by 2 x plus root 3 by 2 into y is equal to 4 can be written as x cos 120 degree plus y sine 120 degree is equal to 4. This is the reduced normal form of the given equation. On comparing this equation with x cos omega plus y sine omega is equal to p, we find that p is equal to 4 that is perpendicular distance from origin is equal to 4. And the angle between perpendicular and the positive x axis that is omega is equal to 120 degree. So after reducing the given equation into normal form, we have got x cos 120 degree plus y sine 120 degree is equal to 4. And perpendicular distance from the origin is 4. And the angle between perpendicular and positive x axis is 120 degree. This is our required answer. So this completes the session. Bye and take care.