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A circle C has its centre on the line L:2x-y+1=0.The x-axis is a tangent to the circle.The circle cuts the y-axis at two points A and B such AB=2√5.Find the two possible equations of the circle C.
ans
(x-2/3)^2+(y-7/3)^2=49/9
(x+2)^2+(y+3)^2=9
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2009-06-03 8:20 am
回答 (2)
2009-06-03 8:45 am
2009-06-04 2:34 am
Let the equation of the circle C be x2 + y2 + fx + gy + h = 0.
Centre on the line 2x-y+1=0:
2(f/-2) - (g/-2) + 1 = 0, g = 2f - 2 ... (1)
The x-axis is a tangent:
When y = 0, △ = f2 - 4h = 0 ... (2)
Cuts the y-axis at two points A and B such AB=2√5:
When x = 0, square of difference of roots = g2 - 4h = (2√5)2 = 20 ... (3)
Solving (1), (2) & (3):
(f, g, h) = (-4/3, -14/3, 4/9) or (4, 6, 4)
Equations of the circle C are
x2 + y2 - 4/3x - 14/3y + 4/9 = 0 or
x2 + y2 + 4x + 6y + 4 = 0.
Centre on the line 2x-y+1=0:
2(f/-2) - (g/-2) + 1 = 0, g = 2f - 2 ... (1)
The x-axis is a tangent:
When y = 0, △ = f2 - 4h = 0 ... (2)
Cuts the y-axis at two points A and B such AB=2√5:
When x = 0, square of difference of roots = g2 - 4h = (2√5)2 = 20 ... (3)
Solving (1), (2) & (3):
(f, g, h) = (-4/3, -14/3, 4/9) or (4, 6, 4)
Equations of the circle C are
x2 + y2 - 4/3x - 14/3y + 4/9 = 0 or
x2 + y2 + 4x + 6y + 4 = 0.
收錄日期: 2021-04-22 00:47:14
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090603000051KK00039