Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XI  >>  Math  >>  Conic Sections
Answer
Comment
Share
Q)

Find the distance between the directrices of the ellipse $\large\frac{x^2}{36}+\frac{y^2}{20}$$=1$.

$\begin{array}{1 1}-9\\-\large\frac{1}{9}\\9\\\large\frac{1}{9}\end{array} $

1 Answer

Comment
A)
Toolbox:
  • Distance between the directrices is $\large\frac{a}{e}$
  • Eccentricity =$\large\frac{\sqrt{a^2-b^2}}{a}$
Answer : $9$
Given equation of the ellipse is $\large\frac{x^2}{36}+\frac{y^2}{20}$$=1$
$\therefore a^2=36$
$\Rightarrow a=\pm 6$
$b^2=20$
$\Rightarrow b=\pm 2\sqrt 5$
$\therefore e=\large\frac{\sqrt{a^2-b^2}}{a}$
$e=\large\frac{\sqrt{36-20}}{6}$
$\;\;\;=\large\frac{4}{6}$
$\;\;\;=\large\frac{2}{3}$
Hence the distance between the directrices is $\large\frac{a}{e}$
$\Rightarrow \large\frac{6}{\Large\frac{2}{3}}$$=9$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...