Equation of circle----20分!!!

2011-09-23 9:12 pm

1. consider the circle S: x^2+y^2+2x-2y-3=0 with centre C. Two tangents are drawn to the circle S from the point A(2,0) outside the circle.
a) Find the equations of the two tangentS.

P.S. 請註明步驟!!! Thank!!!

回答 (1)

用戶25975

2011-09-23 10:09 pm

✔ 最佳答案

C is at (-1, 1) and radius of S = √5

Let m be slope of the tangent, then we have its equation:

y/(x - 2) = m

y = mx - 2m

mx - y - 2m = 0

So the distance from C to the tangent should be equal to 2√5, i.w.

|-m - 1 - 2m|/√(m2 + 1) = √5

|3m + 1|/√(m2 + 1) = √5

(3m + 1)2/(m2 + 1) = 5

9m2 + 6m + 1 = 5m2 + 5

4m2 + 6m - 4 = 0

2m2 + 3m - 2 = 0

(2m - 1)(m + 2) = 0

m = 1/2 or -2

Hence 2 tangents have equatinos:

x/2 - y - 1 = 0

x - 2y - 2 = 0

AND

-2x - y + 4 = 0

2x + y - 4 = 0

參考: 原創答案

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