Prove that the line 2x + y + 2 = 0 is tangent to the circle
x^2 + y^2 + 6x +2y +5 = 0
a.maths 問題!!!
2009-09-06 3:16 am
回答 (2)
2009-09-06 3:29 am
✔ 最佳答案
x^2 + y^2 + 6x +2y +5 = 0-----12x + y + 2 = 0------2
From2, y= -2x-2
x^2 + ( -2x - 2 )^2 + 6x + 2 ( -2x - 2 ) + 5=0
x^2 + 4x^2+ 8x + 4+ 6x - 4x - 4 + 5=0
5x^2 + 10x + 5 = 0
x^2 + 2x + 1 = 0
Delta(個三角形符號) = 2^2 - 4(1)(1) = 0
so, the line 與 the circle 交於一點, is tangent to the circle.
參考: ME, 唔知有有打錯
2009-09-06 3:38 am
Centre at (-3, -1), radius = √5
Distance of centre from 2x + y + 2 = 0 is:
|[2(-3) + (-1) + 2/√5] = √5
So the line is a tangent.
Distance of centre from 2x + y + 2 = 0 is:
|[2(-3) + (-1) + 2/√5] = √5
So the line is a tangent.
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