Email
Chat with tutor
logo

Ask Questions, Get Answers

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

Let $(x_1,y_1)$ be the point of intersection of the tangent to the parabola $y^2=4ax$ at the points $t_1$ and $t_2$ . Then $x_1=a{t_1}{t_2}$ and $y_1=a(t_1+t_2)$

Prove that if  $(x_1,y_1)$ be the point of intersection of the tangent to the parabola $y^2=4ax$ at the points $t_1$ and $t_2$ . Then $x_1=a{t_1}{t_2}$ and $y_1=a(t_1+t_2)$

1 Answer

Comment
A)
Let the equation of the two tangents at the points $A(t_1)$ and $B(t_2)$ be $yt_1=x+at_1^2$ and $yt_2=x+at_2^2$
Subtract both the equations $y (t_1-t_2)=a(t_1^2-t_2)y(t_1 -t_2) =a(t_1-t_2)$
Hence $y=a(t_1+t_2)$ Substituting in equal $a(t_1+t_2) t_1=x+at_1^2$
Therefore at $1^2 +t_1 t_2 =x +t_1^2$
Therefore $x=t_1t_2$
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.
...