whats-the-intersiction-of-the-curves-r-1-1-cos-and-r-1-1-cos-

Question Number 136988 by mohammad17 last updated on 28/Mar/21

w h a t s t h e i n t e r s i c t i o n o f t h e c u r v e s r = \frac{1}{1 - c o s θ}

a n d r = \frac{1}{1 + c o s θ} ?

Answered by Ñï= last updated on 28/Mar/21

r = \frac{1}{1 - \cos θ}

\Rightarrow r - r \cos θ = \sqrt{x^{2} + y^{2}} - x = 1 (1)

r = \frac{1}{1 + \cos θ}

\Rightarrow r + r \cos θ = \sqrt{x^{2} + y^{2}} + x = 1 (2)

(2) \land (1)

\Rightarrow x = 0 y = \pm 1

i n t e r s e c t p o i n t s : (0, 1), (0, - 1)

Answered by physicstutes last updated on 29/Mar/21

At the point of intersection, these two

polar curves are equal . That is

\frac{1}{1 - \cos θ} = \frac{1}{1 + \cos θ}

\Rightarrow 1 - \cos θ = 1 + \cos θ

\cos θ = 0 or θ = 2 π n \pm \frac{π}{2}

hence θ = {\frac{π}{2}, - \frac{π}{2}}

points of intersection are (1, \frac{π}{2}) and (- 1, - \frac{π}{2})

Commented by physicstutes last updated on 29/Mar/21