Question 16 c (ii) 2012 paper (1 Viewer)

[mac1996]

Hey guys
Can someone please explain how to do the very last question of the 2012 paper, which is Question 16 c(ii). Sorry I cant show you the question because im on my phone.


Thanks

 

[RealiseNothing]

If then we substitute part (i) in for both and solve:









#

Do you need help with part (iii) and (iv)?

 

[RealiseNothing]

I'm going to assume you do since you said the last question:

iii) We are given



Now since 'n' and 'k' are integers, then the LHS is greater than the RHS by atleast 1. Hence we can get rid of the on the LHS and the strict inequality will still hold:





(note that and so the RHS>0 and we can take the square root without any worries). #

 

[Kurosaki]

I think he's asking about 2U maths lol

 

[RealiseNothing]

I think he's asking about 2U maths lol

Holy shit, I thought I was in the MX2 section.

 

[RealiseNothing]

I've probably just scared the fuck out of him.

 

[Kurosaki]

 

[Shazer2]

I've probably just scared the fuck out of him.

You scared the fuck out of me.

 

[louielouiee]

I'm certain that almost every HSC student last year just looked at that question and just thought to themselves, fuck that.


I know I did

 

[gosfa747]

check the sample answers on the board of studies website

 

[mac1996]

I've probably just scared the fuck out of him.

AHAHAHA u kinda did lol
And ye its 2u
Btw I never knew the 4u exam had 16 questions

 

[twinklegal19]

AHAHAHA u kinda did lol
And ye its 2u
Btw I never knew the 4u exam had 16 questions

It's the same format at the 2U one

 

[mac1996]

check the sample answers on the board of studies website

Their sample answer didnt make sense to me.

 

[Sy123]

Hey guys
Can someone please explain how to do the very last question of the 2012 paper, which is Question 16 c(ii). Sorry I cant show you the question because im on my phone.


Thanks

From the previous question, remember our quadratic equation.



The solutions to this equation are the y-coordinates of the intersection of the parabola and circle. But it is evident that at both intersections they have the same y-coordinate, and hence discriminant is zero (this is how you do the first part).

It is asking us to prove a restriction that c must adhere to, in order to satisfy 'the circle touches the parabola at exactly two points'.
These intersection points must be positive, our solutions to the quadratic equation must be greater than zero, so if we solve the quadratic in y.



This solution must be greater than zero.





But that isn't quite the answer yet, we need to examine what happens when c=1/2, we see that if this is the case, then y=0. But this can't be the case, because then the intersection is at the origin only, which doesn't satisfy the condition in the question 'touches the parabola at exactly 2 points'. So we must discount c=1/2

Hence c > 1/2

 

[lee337]

I'm certain that almost every HSC student last year just looked at that question and just thought to themselves, fuck that.


I know I did

You know me too well.