AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

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