(a) Given two points A(2,0) and B(4,2), find the equation of the perpendicular bisector of AB.
(b) Hence, or otherwise, find the equation of the circle with centre lying on the straight line L: y = 2x - 11 and passing through A and B.
Circle
2010-12-09 11:18 pm
回答 (1)
2010-12-09 11:40 pm
✔ 最佳答案
a)The slope of the equation * The slope of AB = - 1 ,The slope of the equation * (2 - 0) / (4 - 2) = - 1The slope of the equation = - 1The perpendicular bisector of AB passing through the mid point of AB , i.e. [(2+4)/2 , (0+2)/2] = (3 , 1)So the required equation is (y - 1)/(x - 3) = - 1==> y - 1 = 3 - x==> x + y - 4 = 0b)Since the centre lying on both line : x + y - 4 = 0 and L : y = 2x - 11.The centre is the intersection point of x + y - 4 = 0...(1) and y = 2x - 11....(2) ,Sub (2) into (1) :x + 2x-11 - 4 = 0x = 5
y = 2*5 - 11 = - 1The centre of the circle is (5 , - 1)radius square = (5 - 2)^2 + (- 1 - 0)^2 = 10The equation of the circle is (x - 5)^2 + (y + 1)^2 = 10
收錄日期: 2021-04-21 22:24:41
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101209000051KK00528