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樂仔 2007-05-15 00:38

A.Maths高手請來

Find the equation of the cirlce with the center on the x-axis and touching the line 2x-y-1=0 at (1, 1)


可唔可以教下我點做
感謝

垃圾桶 2007-05-15 00:41
center (x,0)
touching (1,1)

general form一代....入去

2條式2個unknown....


呢個方法唔得....

樂仔 2007-05-15 00:42
試緊...

樂仔 2007-05-15 00:42
噢...我再諗諗

jov 2007-05-15 00:42
x^2+y^2+Dx+Ey+F

用個center(1, 1)搵到D,E...

跟住個radius=個center同條line既distance...搵埋F..

樂仔 2007-05-15 00:42
連個radius點搵都唔知

樂仔 2007-05-15 00:43
引用第4樓j摩連奴.狂妄2007-05-15 00:42發表的“”:
x^2+y^2+Dx+Ey+F
用個center(1, 1)搵到D,E...
跟住個radius=個center同條line既distance...搵埋F..

center唔係(1, 1)丫

jov 2007-05-15 00:44
引用第5樓樂仔2007-05-15 00:42發表的“”:
連個radius點搵都唔知 [表情]

書有講架..= =

radius=1/2(D+E-4F)^1/2

唔知有冇記錯

樂仔 2007-05-15 00:46
我連題目都未解得掂
Find the equation of the cirlce {with the center on the x-axis} {and touching the line 2x-y-1=0 at (1, 1)}

or

Find the equation of the cirlce with the center {on the x-axis and touching the line 2x-y-1=0 at (1, 1)}




jov 2007-05-15 00:47
引用第6樓樂仔2007-05-15 00:43發表的“”:
center唔係(1, 1)丫 [表情]

咁...

center(h,0)同(1, 1)既distance=個center同條line既distance

搵到個h吧

jov 2007-05-15 00:48
引用第8樓樂仔2007-05-15 00:46發表的“”:
我連題目都未解得掂
Find the equation of the cirlce {with the center on the x-axis} {and touching the line 2x-y-1=0 at (1, 1)}
or
.......

上面呀

樂仔 2007-05-15 00:48
引用第9樓j摩連奴.狂妄2007-05-15 00:47發表的“”:
咁...
center(h,0)同(1, 1)既distance=個center同條line既distance
.......

center同條line既distance應該搵唔到-0-
除非係in terms一d野...

樂仔 2007-05-15 00:49
引用第10樓j摩連奴.狂妄2007-05-15 00:48發表的“”:
上面呀 [表情]

icic...

樂仔 2007-05-15 00:50
引用第9樓j摩連奴.狂妄2007-05-15 00:47發表的“”:
咁...
center(h,0)同(1, 1)既distance=個center同條line既distance
.......

係唔係即係咁

(1-h)^2+(-1)^2= d

垃圾桶 2007-05-15 00:50
引用第11樓樂仔2007-05-15 00:48發表的“”:
center同條line既distance應該搵唔到-0-
除非係in terms一d野...

ya

jov 2007-05-15 00:52
引用第13樓樂仔2007-05-15 00:50發表的“”:
係唔係即係咁
(1-h)^2+(-1)^2= d

ya..

個center同條line既distance

有條公式搵架...應該係代入去..睇下書啦..應該有寫

樂仔 2007-05-15 00:53
引用第14樓垃圾桶2007-05-15 00:50發表的“”:
ya

都係要...in terms 一d野

樂仔 2007-05-15 00:54
引用第15樓j摩連奴.狂妄2007-05-15 00:52發表的“”:
ya..
個center同條line既distance
.......

我有背條公式...依家試緊代..唔該你先

樂仔 2007-05-15 00:54
做唔到...

BBF 2007-05-15 00:58
咁淺我都唔記得

都唔知我點考 PURE MATH C返黎

kylau 2007-05-15 00:58
Centre of circle at (h,0)

So eq of circle is (x-h)^2 + y^2 = r^2 .............(*)

Intercept with 2x-y-1=0 at (1,1)

So sub (1,1) into (*) get one equation

For line 2x-y-1=0, slope = 2

So use slope between (h,0) and (1,1) = -1/2 to have the second equation.

Solve for h first, then r, then eq of circle is done.

垃圾桶 2007-05-15 00:59
引用第19樓ballballfull2007-05-15 00:58發表的“”:
咁淺我都唔記得 [表情]
都唔知我點考 PURE MATH C返黎 [表情]

超勁...我果時a maths緊緊合格.....

樂仔 2007-05-15 01:00
引用第20樓kylau2007-05-15 00:58發表的“”:
Centre of circle at (h,0)
So eq of circle is (x-h)^2 + y^2 = r^2 .............(*)
Intercept with 2x-y-1=0 at (1,1)
So sub (1,1) into (*) get one equation
For line 2x-y-1=0, slope = 2
So use slope between (0,h) and (1,1) = -1/2 to have the second equation.
Solve for h first, then r, then eq of circle is done.
.......

呢度開始唔明

垃圾桶 2007-05-15 01:01
slope between (0,h) and (1,1) = -1/2

呢2點之間個slope係-1/2 x埋90 degree

2 point form就搵到h

之後

樂仔 2007-05-15 01:01
哦...兩個slope乘埋=-1 ..明白

BBF 2007-05-15 01:02
引用第22樓樂仔2007-05-15 01:00發表的“”:
呢度開始唔明 [表情]


two line, 90 degree

jov 2007-05-15 01:02
引用第22樓樂仔2007-05-15 01:00發表的“”:
呢度開始唔明 [表情]

For line 2x-y-1=0, slope = 2

So use slope between (0,h) and (1,1) = -1/2 to have the second equation.

兩個slope成90度....乘埋=-1

kylau 2007-05-15 01:02
tangent is prependicular to radius,

So ....

slope between (0,h) and (1,1) = -1/2

樂仔 2007-05-15 01:04
引用第27樓kylau2007-05-15 01:02發表的“”:
tangent is prependicular to radius,
So ....
slope between (0,h) and (1,1) = -1/2

嗯...我依家搵到個h出黎

之後就搵r?

垃圾桶 2007-05-15 01:04
引用第28樓樂仔2007-05-15 01:04發表的“”:
嗯...我依家搵到個h出黎
之後就搵r?

當然啦

有center了,center同1,1.....個距離仲唔係radius

BBF 2007-05-15 01:05
我投降....係忘記晒,...真係 "還返晒比老師" 啦

樂仔 2007-05-15 01:06
我計到h= 3/2
r= square root 5/2
有冇錯到

kylau 2007-05-15 01:08
correct

Then find the equation of the circle

樂仔 2007-05-15 01:08
都係錯...唉..冇哂心機

樂仔 2007-05-15 01:09
引用第32樓kylau2007-05-15 01:08發表的“”:
correct
Then find the equation of the circle

點解計唔到既

你睇下係唔係咁

(y-3/2)^2 + x^2= 5/4

垃圾桶 2007-05-15 01:09
引用第33樓樂仔2007-05-15 01:08發表的“”:
都係錯...唉..冇哂心機

(書個答案未必岩的)

樂仔 2007-05-15 01:10
我最後計到x^2+y^2-3y+1=0...但係ans唔係咁

kylau 2007-05-15 01:11
I've made a typo mistake

So use slope between (h,0) and (1,1) = -1/2

Should be (0,h) instead of (h,0).

U try once more, sorry

樂仔 2007-05-15 01:12
引用第37樓kylau2007-05-15 01:11發表的“”:
I've made a typo mistake [表情]
So use slope between (h,0) and (1,1) = -1/2
Should be (0,h) instead of (h,0).
.......

你無錯丫
個center係(h,0)喎

死喇...愈整愈亂

kylau 2007-05-15 01:13
Check if h=3, r = root 5

eq is x^2 + y^2 - 6x + 4 =0
--------------------
slope between (h,0) and (1,1) = -1/2

1 / (1-h) = -1/2

h=3

樂仔 2007-05-15 01:14
哦..明喇

h應該係=3..right?

kylau 2007-05-15 01:15
yes, Check if eq is x^2 + y^2 - 6x + 4 =0

樂仔 2007-05-15 01:16
引用第39樓kylau2007-05-15 01:13發表的“”:
Check if h=3, r = root 5
eq is x^2 + y^2 - 6x + 4 =0
--------------------
slope between (h,0) and (1,1) = -1/2
.......


搞掂

thx!!

樂仔 2007-05-15 01:17
呢條其實係第20條...之後既第21條至到26條...通通都唔識

樂仔 2007-05-15 01:19
21) Find the equation of the circle which passes through the point (1, 2) and touches the line x-3y-5=0 at (-1, -2)

樂仔 2007-05-15 01:20
引用第44樓樂仔2007-05-15 01:19發表的“”:
21) Find the equation of the circle which passes through the point (1, 2) and touches the line x-3y-5=0 at (-1, -2)

我想問...果兩個point係唔係對住?
咁可唔可以話...果兩個point既distance就係diameter?

Bun 2007-05-15 01:23
引用第44樓樂仔2007-05-15 01:19發表的“”:
21) Find the equation of the circle which passes through the point (1, 2) and touches the line x-3y-5=0 at (-1, -2)

其實呢d來來去去都不外乎幾個方法=v=

(x-a)^2+(y-b)^2=r^2...

repeated root...


冇理由咁多唔識嫁bo=v=

不如你試多陣先啦

樂仔 2007-05-15 01:25
引用第46樓alvin_bun2007-05-15 01:23發表的“”:
其實呢d來來去去都不外乎幾個方法=v=
(x-a)^2+(y-b)^2=r^2...

.......

3點試到依家喇
我就黎撞牆撞暈佢算

樂仔 2007-05-15 01:26
第一次做功課做到咁燥...不好意思...

Bun 2007-05-15 01:27
引用第48樓樂仔2007-05-15 01:26發表的“”:
第一次做功課做到咁燥...不好意思...

a maths呢d野=v=訓返教精神d再做啦@@


急唔黎~


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