question_answer 94)

Show that normal at any point  to the curve x = a cos + a sin , y = a sin  ? a  cos  is at a constant distance from the origin

Answer:

Given curves are x =                         and y =       a cos             = slope of tangent to give curve               slope of normal to the curve,                         Equation of normal to the curve is                                                               ?.. (1)       Now perpendicular distance of (1) from (0, 0)             Hence the normal to the given curve at any point  is at a constant distances from the origin.