Q.17 Consider two points A(3,1) and C(-1, -1 ).
a)Find the equation of the perpendicular bisector of the line segment
joining A and C.
b)Find the equation of the circle with AC as diameter.
c)If ABCD is a square, find the coordinates of B and D.
**(a)同(b)我都識做..但係去到c我就唔識啦...
之後我睇solution ,佢係將(a)同(b)既答案用黎做substitution之後就
可以搵到the coordinates of B and D.
但我唔明白點解可以咁...請大家詳細指點我!!!PLX!!!
Amaths circle
2009-02-04 12:15 am
回答 (2)
2009-02-04 12:28 am
✔ 最佳答案
(a) 答案 2x + y - 2 = 0(b) 答案 x² + y² - 2x - 4 = 0
(c) 由於 AC 為 diameter of the circle, 如此 AC 的 perp. bisector 亦穿過 circle 的 centre, 所以此線亦為 circle 的 diameter 之一.
而它與 circle 的相交點就是 B 和 D, 因為任何兩條 perpendicular 的 diameter 在 circle 內皆可構成一個 square 的 diagonals.
參考: Myself
2009-02-04 12:29 am
Because the intersection of the perpendicular bisector and the circle will be the co-ordinates of B and D.
收錄日期: 2021-04-13 16:24:19
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