Parametrics Question HELP PLEASE (1 Viewer)

[iStudent]

I've been stuck on this question for a few hours now
Someone please help me

 

[enigma_1]

ahhh it's hard to explain it via typing hold on

 

[HeroicPandas]

Man, you just need to convert words into a beautiful diagram

Once that is done, everything will be clear

 

[enigma_1]

You gotta show the angle between the green lines is 90 degrees. For that, you need the coordinates of the focus. For that you need “a”. We know that a is 1, since the general form is x^2 = 4ay, and hence 4a = 4 :. a = 1 in this case.

So find the focus, then find the gradient of PS and QS and show that when you times the gradient of PS and QS together, they give you -1 indicating the lines are perpendicular :. 90 degrees right angle.

If you don't know how to find coordinates of P and Q, you use the general thingy, I think it's x=2p, y=p^2 for this question ? Soz haven't touched parametrics in a while.

for ii, find the eqn of tangent to P and Q and simultaneous equations to find T. Then use distance formula to prove what they ask you to prove. Always draw a diagram. Sorry if this is messy, would have been better on paper

 

[iStudent]

Yea I already tried doing that except my algebra failed me
When I multiplied the gradients together, I get this complex fraction with many p's
and idk how to simplify it (already tried factorising, etc)

 

[iStudent]

bump (lol)
I'll give an imaginary cookie if anyone can do this hard question!

 

[iStudent]

ok nvm I solved the question (after 2 months, lol)
Thanks everyone who tried !

 

[TL1998]

Question's not hard tbh
i can't really see how you would end up with a 'complex fraction with many p's'

 

[iStudent]

How did you do the question?
I had many p's because I tried to use QS=2PS to form an identity and somehow use this to simplify the gradients. it's wrong though because I realised there's a much easier way of approaching the question. (which I overlooked)