
                ### Instruction: help me answer this question Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
(i) x – √3y + 8 = 0
(ii) y – 2 = 0
(iii) x – y = 4, think step by step
                ### Assistant: The equation of a line in normal form is x cos θ + y sin θ = p, where θ is the angle between the perpendicular and the positive x-axis and p is the perpendicular distance from the origin. To reduce the given equations into normal form, we need to divide both sides of the equation by the constant term so that the coefficient of x and y are 1 and -1, respectively. We then find the value of p by taking the absolute value of the constant term on the right-hand side of the equation. To find the angle θ, we use the fact that the tangent of the angle is the negative reciprocal of the coefficient of y. , The answer is Perpendicular distance from origin = 4, Angle with positive x-axis = 120°
Perpendicular distance from origin = 2, Angle with positive x-axis = 90°
Perpendicular distance from origin = 4/√2, Angle with positive x-axis = 135°
