Locus problem help plaese :) (1 Viewer)

[aoniumz]

The diagram shows a parabola. PQ is any chord parallel to
the directrix. R is a third point on the parabola, and the
lines RP and RQ cut the axis of the parabola at A and B
respectively. Show that the interval AB is bisected by the
vertex of the parabola.

This is from 3 unit Cambridge year 11 book hehe
Any idea how to do this question?

 

[HSC2014]

Well, your goal is to show that OA = OB
And to do this: find eqns of lines RP and RQ and sub x = 0 to find A,B
I'll guide you further if you're still stuck.

 

[kev-kun]

I do have the solution written up if you want it? But if you want a guide best to ask Mr HSC2014 haha....

 

[HSC2014]

I do have the solution written up if you want it? But if you want a guide best to ask Mr HSC2014 haha....

Do show I don't think my way is optimal and there are many approaches to this question!

 

[kev-kun]

Ooh yeah sure:

Hopefully you can read, handwriting and scanner aren't the best...

 

[HSC2014]

Ooh yeah sure:
View attachment 28697
Hopefully you can read, handwriting and scanner aren't the best...

Your handwriting makes mine look almost illegible haha Here's mine, with a slightly different approach (y = kx^2 and no parameters). I think you get redundant in some places, or maybe mine is too short.

 

[kev-kun]

Wow =='' So short!! But effective eh? I probably took the long way since I used parametrics and chord equations. Haha good job on your side.

 

[aoniumz]

Thank you so much!!! I tried the question using something very similar to Kev-kun way, but didn't realise the part p + q = 0

Thankxxxx to both of you!