the equation of circle

[匿名]

2007-09-04 6:41 am

The equationof a circle C is x^2+y^2-10x-8y+18=0.
a)Determine wheather the pointP(1,2) is inside or outside the circle C.
b)A line L passes through the point P. Find the equation of L if L cuts the circle C with
i) the longest chord,
ii) the shortest chord.

回答 (1)

用戶195274

2007-09-04 7:01 am

✔ 最佳答案

x^2+y^2-10x-8y+18=0
(x-5)^2 + (y-4)^2 + 18 - 25 - 16 = 0
(x-5)^2 + (y-4)^2 = 23
Centre (5,4), radius = root(23)
Distance between P and (5,4) = root[(5-1)^2+(4-2)^2] = root(20)

2007-09-03 23:03:43 補充：
(b)(i) Longest chord = the equation passing through P and Centre, i.e. equation of diameter.Equation: y-2 = (4-2)/(5-1) *(x-1)2(y-2) = x-1, i.e. x-2y+3 = 0

2007-09-03 23:04:00 補充：
(ii) Shortest chord = equation which is perpendicular to the equation of diameter passing P.Slope of required equation = -2Equation: y-2 = -2(x-1), i.e. 2x+y-4=0

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