Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Find the equation of the standard rectangular hyperbola whose centre is $(\large-\frac{1}{2} , -\frac{1}{2})$ and which passes through the point $(1 , \large\frac{1}{4})$

1 Answer

Comment
A)
Toolbox:
  • http://clay6.com/mpaimg/toolbox%2021.jpg
  • For the standard rectangular hyperbola,the coordinate axes are taken to the asymptotes and the equation of the hyperbola is $xy=c^2$ .
  • If the centre is at $(h,k)$ with asymptotes parallel to the coordinate axes,the equation is $(x-h)(y-k)=c^2$
Step 1:
The centre of the rectangular hyperbola is at $(-\large\frac{1}{2}.-\large\frac{1}{2})$ with asymptotes parallel to the coordinate axes.
Therefore its equation is of the form $(x+\large\frac{1}{2})($$y+\large\frac{1}{2})=$$c^2$
Step 2:
The point $(1,\large\frac{1}{4})$ lies on the rectangular hyperbola.
Therefore $(1+\large\frac{1}{2})(\large\frac{1}{4}+\frac{1}{2})=$$c^2$
$\Rightarrow c^2=\large\frac{9}{8}$
The equation of the rectangular hyperbola is $(x+\large\frac{1}{2})($$y+\large\frac{1}{2})=$$\large\frac{9}{8}$
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.
...