Question (Circles)
2009-02-15 6:50 am
Consider S: x2 + y2 + (k-8)x + (2k-10)y + (1-4k) = 0, where k is a real number. As k varies, S represents a family of circles passing through two fixed points. Find the coordinates of these two points.
回答 (1)
2009-02-15 7:00 am
✔ 最佳答案
S: x2 + y2 + (k-8)x + (2k-10)y + (1-4k) = 0From the condition
Sub k=8
x2 + y2 + 6y = 31
Sub k=5
x2 + y2 -3x = 19
These two circle passing through two fixed points
So 31-6y=3x+19
3x+6y-12=0
x+2y-4=0
x=4-2y
Sub into x2 + y2 + 6y = 31
y^2-2y-3=0
y=-1 or 3
x=6 or -2
The coordinates of these two points are (6,-1) and (-2,3) respectively
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