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20 Days to Go(-6 Days): Coordinate Geometry ( Circle problem)

April 11, 2018
C is a circle passing through A(-2, 1)and B(-2, 3) . Which of the following cannot be the equation of the diameter of the circle C?
.font-size-custom{ font-size: 18px; line-height: 28px; } A. x+y-8=0
B. x-y-5=0
C. 2x-y+5=0
D. x+y+1=0
20 Days to Go(-6 Days): Coordinate Geometry ( Circle problem)
B

想睇2019年DSE Math LQ同MC既參考答案CLICK呢度啦！

20 Days to Go(-6 Days): Coordinate Geometry ( Circle problem)
唔少同學仔嘅問題係將D式死記硬背，所以見到問題改左少少樣就當然地唔識做喇。我地多番強調，近年考題上多左要同學嘗試畫圖嘅問法，就好似呢題咁。
首先大概畫個圖出來。圖中，直線L係AB的垂直平分線。由於弦的垂直平分線是一定穿過圓心，所以我地知道circle C 的圓心一定在L之上。
20 Days to Go(-6 Days): Coordinate Geometry ( Circle problem)
當同學仔再畫埋其他4條線就會發現，只有B答案的線同L係平行而無相交點。咁意味住無論個圓心係邊，答案B嘅線都無可能穿過圓心，即係B無可能係circle C嘅diameter。
20 Days to Go(-6 Days): Coordinate Geometry ( Circle problem)
同學可能發現，呢個問題考緊嘅，主要係slope 同chord嘅概念。所有直線跟L平行而非L自己本身，都無可能成為diameter。相反，只要直線唔係同L平行，就肯定有機會成為圓的直徑。
20 Days to Go(-6 Days): Coordinate Geometry ( Circle problem)

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