At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
The vertices of ellipse are (−1,0) and (3,0).
The polar equation of an ellipse can be represented as
[tex]r=\frac{ep}{1+ecos\theta}[/tex]
where e is the eccentricity.
Eccentricity, e = [tex]\frac{c}{a}[/tex]
c is the distance from the center to the focus and a is the distance from the center to the vertex
[tex]c=\frac{3-(-1)}{2}[/tex]
⇒ [tex]c=\frac{4}{2}[/tex]
⇒ c = 2
[tex]a=\frac{3+(-1)}{2}[/tex]
⇒ [tex]a=\frac{2}{2}[/tex]
⇒ a = 1
Then, e = [tex]\frac{2}{1}[/tex]
⇒ e = 2
Now, the polar equation of an ellipse becomes as,
⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)
Now plug in a vertex point such as (-1,0) and solve for p,
⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]
⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex] [∵ cos 0 = 1]
⇒ [tex]-1=\frac{2p}{3}[/tex]
⇒ [tex]-3=2p[/tex]
⇒ [tex]p=-\frac{3}{2}[/tex]
Thus the polar equation of an ellipse (1) becomes as,
⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]
⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]
Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
Learn more about polar equation of an ellipse here
https://brainly.com/question/17571182
#SPJ4
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
