3. 求AB為直徑的圓方程
a.A(4,-2),B(-2,-2)
b.A(1,1) ,B(7,9)
4.求下列各圓中的方程
圓中顯示了X軸截距為2,Y軸截距為2
5a.求穿過O(0,0),A(6,0)和B(0,-10)的圓C的方程
b.問P(3,-12)是否在圓C上?
求AB為直徑的圓方程(20分)
2008-10-22 4:06 pm
回答 (2)
2008-10-23 12:58 am
✔ 最佳答案
第 4 題題目只已知兩個條件，尚欠一個條件：例如圓與兩軸相切、或經過圓心或某一點，否則沒有足夠條件計算。2008-10-22 16:58:53 補充：
The answer is as follows:
圖片參考：http://i277.photobucket.com/albums/kk75/uncle_michael/20081022_mat_2.jpg?t=1224665795
2008-10-22 9:31 pm
3a distance between AB=((4 2)^2 (-2 2)^2)^(1/2)=6
radius of circle=1/2(6)=3
((x-4)^2 (y 2))^2=3^2
x^2-8x y^2 4y 11=0
3bdistance between AB=((1-7)^2 (1-9)^2)^(1/2)=10
radius of circle=1/2(10)=5
((x-1)^2 (y-1))^2=5^2
x^2-2x y^2-2y-8=0
4let the centre of circle be (x,y)
radius of circle is 2
(x-2)^2 (y-2)^2=2^2
x^2 y^2-4x-4y 4=0
5a let the equation of circle is x^2 y^2 Dx Ey F=0
subs (0,0), F=0
subs (6,0),D=-6
subs(0,-10), E=10
equation of C : x^2 y^2-6x 10y=0
b sub(3,-12)to equation of C
LHS=15
RHS=0
LHSis not equal to RHS
P(3,-12)否在圓C上
radius of circle=1/2(6)=3
((x-4)^2 (y 2))^2=3^2
x^2-8x y^2 4y 11=0
3bdistance between AB=((1-7)^2 (1-9)^2)^(1/2)=10
radius of circle=1/2(10)=5
((x-1)^2 (y-1))^2=5^2
x^2-2x y^2-2y-8=0
4let the centre of circle be (x,y)
radius of circle is 2
(x-2)^2 (y-2)^2=2^2
x^2 y^2-4x-4y 4=0
5a let the equation of circle is x^2 y^2 Dx Ey F=0
subs (0,0), F=0
subs (6,0),D=-6
subs(0,-10), E=10
equation of C : x^2 y^2-6x 10y=0
b sub(3,-12)to equation of C
LHS=15
RHS=0
LHSis not equal to RHS
P(3,-12)否在圓C上
收錄日期: 2021-04-25 13:39:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081022000051KK00286