IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: immortal on April 20, 2010, 06:36:19 pm

Title: Help in maths p1!
Post by: immortal on April 20, 2010, 06:36:19 pm
Find the values of k for which the line y=kx-2  meets da curve y2=4x-x2
Title: Re: Help in maths p1!
Post by: past-papers on April 20, 2010, 06:57:15 pm
simultaneous equations:

y^2 => k^2x^2 -4kx +4 = 4x - x^2
Title: Re: Help in maths p1!
Post by: nid404 on April 20, 2010, 06:58:27 pm
Quote from: immortal on April 20, 2010, 06:36:19 pm
Find the values of k for which the line y=kx-2  meets da curve y2=4x-x2

Post the paper up
Title: Re: Help in maths p1!
Post by: past-papers on April 20, 2010, 07:00:04 pm
wait, actually you're missing something --> post the whole question
Title: Re: Help in maths p1!
Post by: immortal on April 20, 2010, 07:13:46 pm
I posted da whole question which i got 4 ma Mocks.da only thing i missed out waz dat it waz a [4] marks question.
Title: Re: Help in maths p1!
Post by: student on April 20, 2010, 07:50:16 pm
I didnt do p1, but..

y2=4x-x2 is a circle, isnt it?
With 0=<x=<4.

And y=kx-2 would pass through this circle at k>0 to the infinity.
Title: Re: Help in maths p1!
Post by: tmisterr on April 21, 2010, 03:58:52 pm
Quote from: past-papers on April 20, 2010, 06:57:15 pm
simultaneous equations:

y^2 => k^2x^2 -4kx +4 = 4x - x^2

You probably are missing something but if not continuing from past papers equation

k2x2-x2-4kx-4x+4=0 so as you know if it meets the curve it must either have a repeated root (b2=4ac or it b2>4ac

so (-4k-4)2>or=4*(k2+1)*4
solving this equation gives you k>or=0.
Title: Re: Help in maths p1!
Post by: nid404 on April 21, 2010, 04:32:12 pm
yup that what i did and concluded there is something missing :-\
Title: Re: Help in maths p1!
Post by: immortal on April 21, 2010, 05:27:28 pm
y=kx-2  meets da curve y2=4x-x2, so it has a root.

(kx-2)2=4x-x2
k2x2-4kx+4=4x-x2
k2x2+x2-4kx-4x+4=0
(k2+1)x2-(4k+4)x+4=0

as da eqn haz 1 root b2-4ac=0
(4k+4)2-(4*(k2+1)*4)=0
16k2+32k+16-(16k2+16)=0

but i get 32k=0 which is probably wrong!
any ideas Guyz ???


Title: Re: Help in maths p1!
Post by: student on April 21, 2010, 05:34:13 pm
Quote
Find the values of k for which the line y=kx-2  meets da curve y2=4x-x2

There's not one root.
And y=kx-2 does meet y2=4x-x2 at any values of k>0 or equal to 0..
Otherwise there might be some special 'p1 method' for it?