AP EAMCET Engineering 2011 Solved Paper

Given polar equation of linesin‌θ−cos‌θ=1∕r ......(i)
and point (2,π∕6)
Let x=r‌cos‌θ=2.cos‌π∕6=√3
and y=r‌sin‌θ=2.sin‌π∕6=1
The cartesian point is (√3,1).
Now, we change the polar of line into cartesian form
i.e., r‌sin‌θ−r‌cos‌θ=1
⇒ y−x=1 .......(ii)
Equation of perpendicular line to Eq. (ii) is
y+x=λ .......(iii)
which passes through (√3,1)
λ=√3+1
From Eq. (iii), we get
x+y=√3+1
Now, we convert this into polar form
r‌cos‌θ+r‌sin‌θ=√3+1
⇒ sin‌θ+cos‌θ=

√3+1

r