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2017 HSC Mathematics Extension 2 paper thoughts? (1 Viewer)

calamebe

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Can someone please write a solution for 16b
|a|e - |a| = |a|(e-1) = 1

Therefore |a| = 1

a= 1 or a = -1

Oh and also you can do the other vertex:

|a|e + |a| = |a|(1+e) = 1

Therefore |a| = 1/3

a = 1/3 or a = -1/3
 
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calamebe

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Oh wow, I guess I'll retract my previous statement then.
Good on you either way - do you plan on pursuing mathematics in university?
Yeah, wanna double major in math and physics.
 

shervos

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|a|e - |a| = |a|(e-1) = 1

Therefore |a| = 1

a= 1 or a = -1
I don't think so- what about vertices on y axis? You have to deal with a quadratic for those. Also you considered only one vertex on the x axis
 

calamebe

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I don't think so- what about vertices on y axis? You have to deal with a quadratic for those
Vertices on the y axis don't exist though. Sub in x = 0 and you get y^2 = -b^2 which unless y = b = 0, is impossible, and b=0 can't be the case either.

I did forget the other case though which I've fixed up now.
 

shervos

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Vertices on the y axis don't exist though. Sub in x = 0 and you get y^2 = -b^2 which unless y = b = 0, is impossible, and b=0 can't be the case either.
Sorry I messed up there- forgot this was a hyperbola not an ellipse.
 

pikachu975

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|a|e - |a| = |a|(e-1) = 1

Therefore |a| = 1

a= 1 or a = -1

Oh and also you can do the other vertex:

|a|e + |a| = |a|(1+e) = 1

Therefore |a| = 1/3

a = 1/3 or a = -1/3
Damn didn't know a could be negative only got half the solutions
 

calamebe

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Damn didn't know a could be negative only got half the solutions
I'm not sure if they'd require that honestly, a and b are usually assumed to be positive anyway. I just did that for completeness.
 

calamebe

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Damn. Are you sure? Isn't 'a' theoretically defined as the length of the semi-major axis so it can't be negative?
I'm guessing, either I'm wrong in doing the negative, or even if you can technically do a negative they won't care about it. Like, I won't pretend to know all the definitions in conics, so you could totally be right. And in that case doing the negative is wrong.
 

MaxATARLoading

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Can someone post the answers for Questions 8, 9 and 10 in MCQ? I got B, D and C respectively
 

InteGrand

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Damn. Are you sure? Isn't 'a' theoretically defined as the length of the semi-major axis so it can't be negative?
As written in the question, a can be negative.

However, once you get the positive solutions for a, getting the rest of the solutions is trivial since you just negate the positive ones.

Since the question was only 2 marks, in my opinion, they should just give the full marks if you get the correct positive values (since getting the negative values isn't really the hard part or point of the question).
 

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