a line is drawn from a fixed point C(-4,1) to a variable point B on the y-axis.From point B, a line perpendicular to BC is drawn to cut the x-axis at A.P(x,y)is the mid point of AB.
a.)Express the coordinates of A and B in term of x and y.
b.)Find the equation of the locus of P.
locus(2)
2011-04-19 5:34 am
回答 (2)
2011-04-19 7:07 am
✔ 最佳答案
a)Let A be (a , 0) , B be (0 , b) ,Since P(x,y)is the mid point of AB ,x = (a + 0)/2 = a/2a = 2xy = (0 + b)/2 = b/2
b = 2yA is (2x , 0)B is (0 , 2y)
b)Since CB 丄 BA ,Slope of CB * Slope of BA = - 1(1 - 2y) / (- 4 - 0) * (2y - 0) / (0 - 2x) = - 1(1 - 2y)(2y) = (- 1)(- 4)(- 2x)2y - 4y² = - 8x2y² - y - 4x = 0
The locus of P(x , y) is 2y² - y - 4x = 0
2011-04-19 20:40:07 補充：
The question say :
From point B, a line {perpendicular} to BC is drawn ......
2011-04-20 4:36 am
why CB 丄 BA ???
收錄日期: 2021-04-21 22:23:34
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