Family of lines
2012-10-11 3:49 pm
For the family of lines y = mx + a + bm where a and b are constants and m is a variable. Find the common point of the family.
回答 (2)
2012-10-11 4:39 pm
✔ 最佳答案
y = mx + a + bm(-y + a) + m(x + b) = 0
Hence the common point of the family is the point of intersection between -y + a = 0 and x + b = 0, i.e. (-b, a)
參考: 原創答案
2012-10-11 5:14 pm
As the common point is independent of m, that is,
y = mx + a + bm
==> (x + b)m + (a - y) = 0
so the coefficient of m term and constant term must be 0, ie
x = -b and y = a
So the common point of the family is (-b, a).
y = mx + a + bm
==> (x + b)m + (a - y) = 0
so the coefficient of m term and constant term must be 0, ie
x = -b and y = a
So the common point of the family is (-b, a).
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