Question

Find the eccentricity e and the distance ldI from the pole to the directrix of the conic

Answer 1

Answer:

The answer is "eccentricity = 0.5 and distance = 60".

Step-by-step explanation:

Given value:

$\bold{r=\frac{420}{ -14 +7 \sin \theta}}$

Standard equation formula:

$\bold{\to r=\frac{ep}{1- e \sin \theta}}$

$\to r=\frac{\frac{420}{-14}}{1- \frac{7}{14} \sin \theta}\\\\\to r=\frac{ -30 }{1- \frac{1}{2} \sin \theta}\\\\\to r=\frac{ -30 }{1- 0.5 \sin \theta}$

$\boxed{ r=\frac{-30 }{1- 0.5 \sin \theta}}$

compare the above value with the Standard equation:

$\to e=0.5 \\ \to ep= -30$

calculating the value of p:

$\to 0.5 p= -30\\\\\to p= \frac{-30}{0.5}\\\\\to p= \frac{-300}{5}\\\\\to p= - 60$

eccentricity  (e) = 0.5

distance = - 60

distance |d| =  60