-
Finished your HSC? Check out our University Discussion, Non-School forums or help out next year's HSC students! -
YOU can help the next generation of students in the community! Share your trial papers and notes on our Notes & Resources page
Annoyingly hard q (1 Viewer)
- Thread starter darlking
- Start date
- Joined
- Feb 16, 2005
- Messages
- 8,393
- Gender
- Male
- HSC
- 2006
When solving for the points of intersection
and
^2=r^2)
We have
^2=r^2\\\\\Rightarrow y^2+(1-2c)y+c^2-r^2=0)
Since the circle is tangent symmetrically the two points of contact must have the same y-value. Hence there is only one solution in y to the equation above. If there is only one solution the discriminant must be zero.
^2-4(c^2-r^2)=0\\\\\Rightarrow 4c=1+4r^2)
When you actually solve the equation for y using the quadratic formula and the result in (i) you get
However, from the diagram it is pretty obvious thay y must be positive so
and
We have
Since the circle is tangent symmetrically the two points of contact must have the same y-value. Hence there is only one solution in y to the equation above. If there is only one solution the discriminant must be zero.
When you actually solve the equation for y using the quadratic formula and the result in (i) you get
However, from the diagram it is pretty obvious thay y must be positive so
Makematics
Well-Known Member
you couldnt find any solutions to a 2012 hsc paper? :S check out itute or something next time lol
luvglee4lyfe
Member
- Joined
- Jul 5, 2013
- Messages
- 35
- Gender
- Female
- HSC
- 2013
Hey Makematics, what's itute?
SpiralFlex
Well-Known Member
- Joined
- Dec 18, 2010
- Messages
- 6,960
- Gender
- Female
- HSC
- N/A
They have 'sample' VCE mainly but also HSC Mathematics solutions. Here: http://www.itute.com/download-free-vce-maths-resources/free-maths-exams/
I have not checked it out yet so don't know how trustworthy they are.
luvglee4lyfe
Member
- Joined
- Jul 5, 2013
- Messages
- 35
- Gender
- Female
- HSC
- 2013
Thank you!