Question

let the perpendicular distance of a line L from the origin l = 5 and let this perpendicular make an angle @ = pi/6 with the x axis. Determine the normal equation of l?
Plz show me working

Answer 1

pi/6 = 30 degrees
our lines go though a point 5 units along there from origin
x = 5 cos 30
y = 5 sin 30
that 30 degree line has slope sin30/cos30 = .577
the perpendicular has slope
-1/.577 = - 1.732
so line is of form
y = -1.732 x + b
now put in y = 5 sin 30 and x = 5 sin 30 to get b