Equation of the line in normal form

We can clearly see a line ‘a’ whose equation is lx + my = n. We also see p which is the length of the perpendicular on the line from the origin and α which is the angle made by this perpendicular with the positive x -axis. As we change the values of α and p using their corresponding slide bars, we can observe how the position of the line changes
Questions to think about: 1. Fix the value of α and change the value of p. What do we observe? 2. Fix the value of p and change the value of α. What do we observe? 3. Input values for \(cos\alpha \), \(sin\alpha \)and p in the equation \[x cos \alpha + y sin \alpha = p\]and compare the result with the given equation of ‘a’ which is lx + my = n