The equation of normal at any point θ to the curve $$x=acos$$⁡θ$$+a$$ θ$$sin$$⁡θ, $$y=asin$$⁡θ−a θ$$cos$$⁡θ is always at a distance of

Question

The equation of normal at any point θ to the curve $$x=acos$$⁡θ$$+a$$ θ$$sin$$⁡θ, $$y=asin$$⁡θ−a θ$$cos$$⁡θ is always at a distance of

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$$x=acos$$⁡θ$$+a$$θ$$sin$$⁡θ,$$y=asin$$⁡θ−aθ$$cos$$⁡θ$$dydx=a$$θ$$sin$$⁡θaθ$$cos$$⁡θ$$=$$$$sin$$⁡θ$$cos$$⁡θSlope of normal $$=$$−$$cos$$⁡θ$$sin$$⁡θEquation of normal at θy−[asin⁡θ−aθ$$cos$$⁡θ]$$=$$−$$cos$$⁡θ$$sin$$⁡θ[x−(acos$$⁡θ$$+a$$θ$$sin$$⁡θ$$)]ysin⁡θ−$$asin2$$⁡θ$$+a$$θ$$sin$$⁡θ$$cos$$⁡θ$$=$$−xcos⁡θ$$+acos2$$⁡θ$$+a$$θ$$sin$$⁡θ$$cos$$⁡θxcos⁡θ$$+ysin$$⁡θ−$$a=0The$$ distance from origin to the $$normal=$$|−a|$$cos2$$⁡θ$$+sin2$$⁡θ$$=a$$

The equation of normal at any point $θ$ to the curve $x = acos θ + a θsin θ, y = asin θ - a θcos θ$ is always at a distance of

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The equation of normal at any point θ to the curve x=acos⁡θ+a θsin⁡θ, y=asin⁡θ−a θcos⁡θ is always at a distance of

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The equation of normal at any point $θ$ to the curve $x = acos θ + a θsin θ, y = asin θ - a θcos θ$ is always at a distance of