Question

question 28 · 1 point
find the polar equation of a parabola with eccentricity 1, and directrix x = 1.
select the correct answer below:
o r = \frac{1}{1 - \cos\theta}
o r = \frac{1}{1 - \sin\theta}
o r = \frac{1}{1 + \sin\theta}
o r = \frac{1}{1 + \cos\theta}

Explanation:

Step1: Recall polar - conic formula

The polar equation of a conic with eccentricity $e$ and directrix $x = d$ is given by $r=\frac{ed}{1+e\cos\theta}$.

Step2: Identify given values

We are given that $e = 1$ and $d = 1$ (since the directrix is $x = 1$).

Step3: Substitute values into formula

Substitute $e = 1$ and $d = 1$ into $r=\frac{ed}{1+e\cos\theta}$, we get $r=\frac{1\times1}{1 + 1\times\cos\theta}=\frac{1}{1+\cos\theta}$.

Answer:

D. $r=\frac{1}{1 + \cos\theta}$