Respuesta :
Answer:
The answer is "eccentricity = 0.5 and distance = 60".
Step-by-step explanation:
Given value:
[tex]\bold{r=\frac{420}{ -14 +7 \sin \theta}}[/tex]
Standard equation formula:
[tex]\bold{\to r=\frac{ep}{1- e \sin \theta}}[/tex]
[tex]\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}\\\\[/tex]
[tex]\boxed{ r=\frac{-30 }{1- 0.5 \sin \theta}}[/tex]
compare the above value with the Standard equation:
[tex]\to e=0.5 \\ \to ep= -30\\[/tex]
calculating the value of p:
[tex]\to 0.5 p= -30\\\\\to p= \frac{-30}{0.5}\\\\\to p= \frac{-300}{5}\\\\\to p= - 60[/tex]
eccentricity (e) = 0.5
distance = - 60
distance |d| = 60
