Normal meets the curve again

[Jiaxuannnnnn]

I have no idea how to do the question (b)

This is my solution for (a)

Can anyone help me to solve the question by giving some tips? ?‍?‍

 

[Steven G]

Why not eliminate t from x = 2t/(t+1) and y = t^2/(t+1)? This will give you y in terms of x. Then you can see the other point of intersection.

 

[Jiaxuannnnnn]

How to find the other point of intersection? ?

 

[Harry_the_cat]

Take your equation of the normal from the last line in post #1 and your Cartesian equation from post #3 and solve simultaneously. Expect one solution to be P. The other solution will be Q.

 

[Harry_the_cat]

Actually, I wouldn't have taken Jomo's advice (sorry Jomo). I would have simply substituted the parametric equations for x and y into the equation of the normal you found in post#1, and then solved for t. One solution will be t=1 which will give P, the other solution will give Q.

 

[Steven G]

Actually, I wouldn't have taken Jomo's advice (sorry Jomo). I would have simply substituted the parametric equations for x and y into the equation of the normal you found in post#1, and then solved for t. One solution will be t=1 which will give P, the other solution will give Q.

I knew there was a better approach but could not think of it. Thanks Harriet.