amaths - Ans.fyi 參考答案

amaths

2007-12-15 10:58 pm

The circles C1:x^2+y^2+4x-2y+1=0
C2:x^2+y^2+10x+4y+F=0
intersect each other at two points P and Q,where the equation of the line PQ is x+y+3=0
(a)Find the value of F
(b)M is an external point on C1 and C2.If M lies on the line PQ,show that the length of the tangent from M to C1 is equal to the length of tangent from M to C

回答 (1)

Ben Chong

2007-12-15 11:45 pm

✔ 最佳答案

(a)
Common chord=C2 - C1 (C1 - C2 都得,你鐘意)
6X + 6Y + F-1 = 0
X + Y + (F-1)/6 =0
(F -1)/6 =3
F = 19
(b)
因為　lies on PQ,
所以 M=(x, -x-3)
radius of c1=2 (用公式)
centre of c1=(-2,1) (用公式)

radius of c2 = (開方40)/2 (用公式)
centre of c2=(-5,-2) (用公式)

因為tangent同radius會形成90度,所以用pyth就搵倒tangent ge length
length of tangent form M to C1=(x+2)^2 + (-x-3+2)^2 - 2^2

.. .. . .. .... .... ... to c2=(x+5)^2 + (-x-3+2)^2 - { (開方40)/2 } ^2
之後就會計倒2條length係一樣(in terms of x)

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