A.Maths Locus... [復制鏈接]

1. Q is a variable point on the curve xy=4. OQ is joined and produced to P such that PQ=0.5OQ, where O is the origin. Find the equation of the locus of P.

2. From a variable point P, perpendiculars are drawn to the line y=2x and the x-axis cutting them at M and N respectively. If PM=5^1/2PN, find the equation of the locus of P.

5^1/2即係5 square root

唉...識做既幫下我
就黎灰到喊...

Q2

Let P = (x,y), M = (b, 2b), N = (x,0)

Slope of OM =2, So Slope of PM = -1/2
=> y-2b / x-b = -1/2
=> x+2y-5b =0 .........(1)

PM=root 5 x PN

So PM square = 5x PN square

=> (x-b)^2 + (y-2b)^2 = 5y^2 ...........(2)

Solving (1) and (2), get b=0 (rej) or y=b

Hence x=3b, and since y=b, get LOCUS of P is x=3y

Q1

Let P= (x,y) , then Q= (2x/3, 2y/3)

Since Q lies on xy=4

So (2x/3)(2y/3)=4, get xy=9

So locus of P is xy=9

萬分感謝
好在有你...

其實除左呢兩條我仲有幾條locus都係唔識做...er...介唔介紹我係度問埋?
(如果你唔得閒既話唔緊要ga..唔駛理我 )

Q2果度...
Solving (1) and (2)果PART...係唔係要將(1)果條式轉做b係subject...再代入(2)果條式既b入面?

引用第4樓樂仔於2007-07-05 22:03發表的“”:
Q2果度...
Solving (1) and (2)果PART...係唔係要將(1)果條式轉做b係subject...再代入(2)果條式既b入面?

no need, just take y-2b / x-b = -1/2

Hence x-b = -2(y-2b) 就ok

咁代x-b 做-2(y-2b) 入(2), much faster

引用第5樓kylau於2007-07-05 22:05發表的“”:
no need, just take y-2b / x-b = -1/2
Hence x-b = -2(y-2b) 就ok
.......

係唔係會變左咁樣:
(4b-2y)^2+(y-2b)^2=5y^2

引用第2樓kylau於2007-07-05 21:49發表的“”:
Q1
Let P= (x,y) , then Q= (2x/3, 2y/3)
Since Q lies on xy=4
.......

做到啦

del

引用第1樓kylau於2007-07-05 21:44發表的“”:
Q2
Let P = (x,y), M = (b, 2b), N = (x,0)
Slope of OM =2, So Slope of PM = -1/2
.......

我answer key度話有兩個答案...x-3y=0同x+2y=0...點解既
我淨係跟你方法...計到x-3y=0

引用第6樓樂仔於2007-07-05 22:10發表的“”:
係唔係會變左咁樣:
(4b-2y)^2+(y-2b)^2=5y^2

yes, 一抽就可以有common term, 約左個5, 快好多


其他的方法都一樣, 唔識再問

引用第9樓樂仔於2007-07-05 22:24發表的“”:
我answer key度話有兩個答案...x-3y=0同x+2y=0...點解既 [表情]
我淨係跟你方法...計到x-3y=0

x+2y-5b =0

如果b=0 不rej, 會出x+2y=0, though it doesn't make sense when u draw a graph to see

哦!!!
會唔會係...y=0唔駛reject?!

引用第11樓kylau於2007-07-05 22:26發表的“”:
x+2y-5b =0
如果b=0 不rej, 會出x+2y=0, though it doesn't make sense when u draw a graph to see

係喎!
M果個point係(b,2b)丫嘛...如果b係0...咁應該做唔到

呢條我聽日返學問阿sir丫...
你得唔得閒幫我解多幾條