Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

The locus of a point $p(\alpha, \beta)$ moving under the condition that the line $y=\alpha x + \beta$ is a tangent to the hyperbola $\large\frac{x^2}{a^2} -\frac{y^2}{b^2}$$=1$ is

$\begin{array}{1 1}(A)\;a\; hyperbola \\(B)\;a\; parabola \\(C)\;an\; ellipse \\(D)\;a \;circle \end{array}$

1 Answer

Comment
A)
If $ y=mx+c$ is tangent to hyperbola, then
$c^2=a^2m^2-b^2$
=> $ \beta^2=a^2 \alpha^2 -b^2$
$\therefore $Locus of P is $a^2x^2-y^2=b^2$
Which is a hyperbola.
Hence A 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.
...