Given: Passing throgh the point
(acos3θ,αsin3θ) and perpendicular to the line xsecθ+y cosecθ=α
Slope of line xsecθ+y cosecθ=α is
m=−tanθ
⇒Slope of the required straight line is cotθ
⇒y=cotθ x+c
It passes through (acos3θ,αsin3θ)
c=αsin3θ−αcos3θcotθ
c=−αcos2θsinθ
y=cotθ x−αcos2θsinθ
∴xcosθ−ysinθ=αcos2θ