The equations of straight line are, x‌sin‌θ+(1−cos‌θ)y=a‌sin‌θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) And, x‌sin‌θ−(1+cos‌θ)y=−a‌sin‌θ‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) Subtract equation (II) from (I), (1−cos‌θ)y+(1+cos‌θ)‌‌=2a‌sin‌θ y[1−cos‌θ+1+cos‌θ]‌‌=2a‌sin‌θ y‌‌=a‌sin‌θ From equation (I) x‌sin‌θ+(1−cos‌θ)a‌sin‌θ‌‌=a‌sin‌θ sin‌θ[x+(1−cos‌θ)a]‌‌=a‌sin‌θ x+a−a‌cos‌θ‌‌=a x−a‌cos‌θ‌‌=0 x‌‌=a‌cos‌θ Now x2+y2=(a‌cos‌θ)2+(a‌sin‌θ)2 x2+y2=a2cos2θ+a2sin2θ x2+y2=a2(cos2θ+sin2θ) x2+y2=a2 Thus, the above equation represents a circle