Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Find curve in $x-y$ plane which passes through$(1,1)$ . Intersects line $y=x$ at right angle at that point and satisfies $xy''+2y''=0$

$(a)\;y=\frac{1}{x^2} \\ (b)\;y = \frac{1}{x} \\ (c)\;y=0 \\ (d)\;y=x^2 $

1 Answer

Comment
A)
$y'= t$
$y''=t'$
$xt'+2t=0$
$x \large\frac{dt}{dx}$$=-2t$
$\large\frac{dt}{t}=\frac{-2 dx}{x}$
$\log t = -2 \log x +\log c$
$t= \large\frac{c}{x^2}$
$\large\frac{dy}{dx}=\frac{c}{x^2}$
$dy =\large\frac{c dx}{x^2}$
$y= \large\frac{-c}{x}$$+c_1$
It satisfies $(1,1)$
$1=-c+c_1$
Curve intersects the line $y=x$ at right angle means it is normal to curve.
So, $\large\frac{dy}{dx}=\frac{c}{x^2}$$=-1$
$c=-1$
So, $c_1=0$
So, $y= \large\frac{1}{x}$
Hence b is the correct answer.
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.
...