数学Paper 1讨论专区

lonely_world

原帖由 Log 于 9-9-2009 02:54 PM 发表
mid point ?got problem ma?
i did already ok
shape?i told u already?!

你做给我看..可以吗?
那个curve是U 还是 п?
然后是在哪一个quadrant?

Log

U shaped quadrant ll for both this graphs k?

lonely_world

原帖由 Log 于 9-9-2009 03:11 PM 发表
U shaped quadrant ll for both this graphs k?

一个有过x axis..一个没有?
酱的话..另外一个的min point 不是不对了?

Log

yes 就是不一样min pont!这是因为values for a b and c in D>0 and D<0 not same

Dicardo

let y = -&#8710;/4a
&#8710; > 0
-&#8710; < 0
-&#8710;/4a < 0
y < 0

let y=-&#8710;/4a
&#8710; < 0
-&#8710; > 0
-&#8710;/4a > 0
y > 0

idontwant2b

a point Q lies on the curve xy=12 and O is the origin. Find the equation of the locus of the midpoint of OQ.

有谁可以教教下吗？
我不知道要怎样做到答案那边。

（答案：xy=3）

meiling

好像是这样做。。

nkrealman

P(ap^2,2ap) and Q(aq^2,2aq) are points on the parabola y^2=4ax and PQ passes through the fixed point (a,0) ; PR and QR are parallel to the x-axis and y-axis respectively ; show that the locus of R has equation xy^2=4a^3

the tangent at P(ap^2,2ap),a point on the parabola y^2=4ax,meets the x-axis at T and S is the fixed point (a,0) ; show that SP=ST

P(ap^2,2ap) and Q(aq^2,2aq) are points on the parabola y^2=4ax and q=2p
TP and TQ are tangent to the parabola,show that the locus of T has the equation 2y^2=9ax

我明白问题问什么，但是不知道从哪里开始啊，快疯了

[ 本帖最后由 nkrealman 于 13-9-2009 06:30 PM 编辑 ]

harry_lim

我最怕coordinate geometry也很讨厌coordinate geometry

harry_lim

明天要考paper 1了
肯定考到很差的

meiling

P(ap^2,2ap) and Q(aq^2,2aq) are points on the parabola y^2=4ax and PQpasses through the fixed point (a,0) ; PQ and OR are parallel to thex-axis and y-axis respectively ; show that the locus of R has equationxy^2=4a^3


OR是什么来的？是不是the fixed point (a,0)？

nkrealman

打错了，是PR和QR才对

[ 本帖最后由 nkrealman 于 13-9-2009 06:29 PM 编辑 ]

nkrealman

不知道我做的对不对。
我找 gradient of PQ，然后找equation of PQ
因为他passes through (a,0) 所以放进去找到 pq=-1

PR and QR are parallel to the x-axis and y-axis respectively
是不是说他们是perpendicular to each other?
我用他们两个的gradient乘起来=-1
找不到答案，是不是方法错了？

接下来那两题都不知道怎样做

harry_lim

zzzzzzzzz.....今天的数学paper 1很难=.="

四月一日的小皮

原帖由 nkrealman 于 13-9-2009 04:46 AM 发表
P(ap^2,2ap) and Q(aq^2,2aq) are points on the parabola y^2=4ax and PQ passes through the fixed point (a,0) ; PR and QR are parallel to the x-axis and y-axis respectively ; show that the locus of R has ...

PR parallel to x－axis，and QR parallel to y－axis
－－－－＞ R （aq＾２，２ap）
PQ :  (p+q)y = 2(x + apq)
         when y=0,  x=a,     pq = -1
let x=aq^2  and y=2ap
    x=a(-1/p)^2 = a/(p^2) ...................1
    y^2 = 4(a^2)(p^2)..........................2
2x1: x(y^2) = 4(a^3)  ...(proven)

let (y^2) = 4ax
differentiate --->  2y(dy/dx)=4a
                            (dy/dx)=2a/y .....................>gradient of tangent
at P,when y=2ap,
                            (dy/dx)=2a/2ap = 1/p
eqn: py = x + a(p^2)
when y = 0, x= -a(p^2)...........> T(-a(p^2),0)
(SP)^2= (ap^2- a)^2 + (2ap - 0)^2
          = (ap^2)^2 - 2(ap)^2 + a^2 +4(ap)^2
          =  (ap^2)^2 + 2(ap)^2 + a^2
          = (ap^2 + a)^2 = (a+ ap^2)^2
          = (a - (-ap^2))^2
          = (ST)^2
   SP = ST

四月一日的小皮

P(ap^2,2ap) and Q(aq^2,2aq) are points on the parabola y^2=4ax and q=2p
TP and TQ are tangent to the parabola,show that the locus of T has the equation 2y^2=9ax

先把gradient of tangent of P and Q找出来。
然后form equation of P and Q。
T是point of intersection of equation of P AND Q。
找出T，然后就找出 locus of T，必要时用q=2p

zolo

1.( lx+3l +1)/( lx+3l -1)< 4
2.( lxl +3)/( lxl -3)>5
3.f(x)=x^4 -(p+1)x^2 +p
  find set of values of p such that f(x) +2x^2 -2=0 has real and distinct root.
4.deduce that if m+ni is a root of ax^2 +bx +c=0 ,then m-ni is another root.

怎样做？
答案∶
1. -3<x<-2 or x>-4/3
2. -9/2<x<-3 or 3<x<9/2
3. p>2 and p not equal to 3

idontwant2b

把4 搬过去减，
然后变成一个整分数后，
用=0的几个interval，
test是正还是负。
第二题也是。
第三题是把f(x)+2x^2 -2 后的quadratic equation
用b^2 - 4ac >0。
第四题是用derive quadratic formula的方法去算，
最后会算到那两个答案其实是conjugate to each other.
m = -b/2a , (+-) ni = i x determinant.

zolo

第三题能用quadratic equation吗？f(x)是quartic equation...用这个方法会找到P>3而不是P>2

白羊座aries

原帖由 idontwant2b 于 28-9-2009 02:20 PM 发表
把4 搬过去减，
然后变成一个整分数后，
用=0的几个interval，
test是正还是负。
第二题也是。
第三题是把f(x)+2x^2 -2 后的quadratic equation
用b^2 - 4ac >0。
第四题是用derive quadratic formula的方法去 ...

第4题不明白..