=−cot‌θ‌. ‌ ∴ The slope of the normal at θ=−‌
1
−cot‌θ
=tan‌θ ∴ The equation of the normal at θ is y−asin‌θ=tan‌θ(x−a−a‌cos‌θ) ⇒y−asin‌θ=‌
sin‌θ
cos‌θ
(x−a−a‌cos‌θ) ⇒y‌cos‌θ−asin‌θ‌cos‌θ ‌‌=xsin‌θ−asin‌θ−asin‌θ‌cos‌θ ‌⇒xsin‌θ−y‌cos‌θ=asin‌θ ‌⇒y=(x−a)‌tan‌θ which always passes through (a,0)