中四 a math

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A circle C:x^2+y^2-4x=0.Two lines PQ1 and PQ2 through the pt P(-2,3) are tangent to the circle C at Q1 and Q2.
a.) The circle C1 pass through the pt P,Q1 and Q2.
    Someone say that the circle C1 must pass through the centre of the circle C. Is correct? Explain your ans.

呢題係咪ｆｉｎｄ左ｑ個兩點後，再ｆｉｎｄ　ｑ之間個ｄｉｓｔａｎｃｅ
證明ｃａｎｄ　ｃ１　ｃｅｎｔｒｅ　之間ｄｉｓｔａｎｃｅ相同．
但我ｆｉｎｄ　到the slope of C1係有開方．．．．．．



The circle C1:x^2+y^2-4x+2=0 and the line L:y=x-2 intersect at two pt A and B.A circle C2 pass through the origin and its centre is at the mid-pt of AB.
a.)A circle C3 has its centre on the X-axis. lt touches C1 externally and touches C2 internally . Find equation C3.




Acicle C1 passes through the pt P(2,1) and is tangent to the line L1: x-2y-5=0 at T(1,-2). Let G be the centre of C1.The line L2:2x-y+4=0 intersects the circle C1 at two pt A and B.
1.)write down the equation of the family of circles passing through A and B.
a.)Find the Equation of the circle C2 which is the smallest one in the family in (1).

抹茶可樂

有人識答就答左先
我走了
今晚見

oscar

先解決第一題：
(1) Find the equation of tangent PQ1 and PQ2.
(2) Find the points Q1 and Q2.
(3) Find the equation of the circle C1 by the points P, Q1 and Q2.
(4) Find the centre of C.
(5) Substitue the centre of C into the equation of C1. Prove whether the centre of C lies on C1.

抹茶可樂

第一條(應該係最快的方法)
Let O be the origin of C
Centre and Radius of C: (2,0),2

OQ1=radius=2
OP=√(2+2)^2-(3-0)^2=5
PQ1=√(-2)^2+3^2-4(-2)=√21

(PQ1)^2+(OQ1)^2
=21+2^2
=25
=(OP)^2

∠PQ1O=90度
By symmetry(對稱性)
OP must pass through the origin of C1
OP is diameter of C1 [converse of ∠ in semi-circle]

O passes through C1
The student is correct

[ Last edited by 落雷 on 2005-8-9 at 02:15 PM ]

抹茶可樂

第二題提示
證明L穿過C1圓心

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第3題又點做呢??
咩係the smallest one in the family in (1).
希望能解答我d問題,唔該哂!!!!

抹茶可樂

當centre of circle 在那條直線上就會 smallest