The equation of a straight line which passes through the point a cos 3 θ , a sin 3 θ and perpendicular to x secθ + y c o s e c θ = a is

Step-by-step solution

We know that a line perpendicular to the line a x + b y + c = 0 is given by b x - a y + k = 0 . Here, given line x sec θ + y cosec θ = a . So, the perpendicular line is x cosec θ - y sec θ + k = 0 . The point a cos 3 θ , a sin 3 θ lies on the line ⇒ a cos 3 θ sin θ - a sin 3 θ cos θ = - k ⇒ a cos 4 θ - sin 4 θ sin θ cos θ = - k ⇒ a cos 2 θ - sin 2 θ cos 2 θ + sin 2 θ sin θ cos θ = - k Using cos 2 &#