2005 Paper Question (1 Viewer)

[passion89]

Hi,
I was wondering if anyone could help me with question 10 a) from the 2005 HSC paper:

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2005exams/pdf_doc/maths_05.pdf


Thank you!

 

[pLuvia]

10a)
(i)Find the gradient of AB letting the gradient be "m" and for the other one find the equation of the line AB, and since y=mx+b sub it in for y and you should get your answer

(ii)Use distance formula finding AB and manipulate your answer and subbing in th values you found for part (i) you get your wanted answer

(iii)I'm thinking you prove that the triangle is right angled and then find the distance of BX and AX then use the normal method for finding the area of a triangle

(iv)Use calculus and find the stationary point for the area and prove it is a maximum

Haven't really looked in depth into the question but that should be the outline of what you should do, for part (iii) there should be a quicker way I think

 

[SoulSearcher]

Haha, I really did like that question, found it easy for a question 10 a).

Alternatively for part 3 of that question, you can use the perpendicular distance formula to find the distance between the line y = mx + b and the point (x, x²), then use the length AB you are given in part ii) to find the area of the triangle normally.

 

[passion89]

Ooooh I got it, thanks heaps!