Question

write the equation of the conic section shown below.

Explanation:

Step1: Recall the polar form of a parabola

The polar form of a conic section is \( r=\frac{ed}{1 + e\cos\theta}\). For a parabola, \(e = 1\).

Step2: Identify the directrix

The directrix is \(x = 7\), so \(d=7\).

Step3: Substitute \(e = 1\) and \(d = 7\) into the polar formula

Substituting into \(r=\frac{ed}{1 + e\cos\theta}\), we get \(r=\frac{1\times7}{1+\cos\theta}=\frac{7}{1+\cos\theta}\).

Answer:

\(r=\frac{7}{1+\cos\theta}\)