急 ! F5 數學軌跡

Bid

2012-07-22 9:50 am

請問以下二條的軌跡圖點畫 :

A) P點移動時與x軸及(-2,5)保持等距.繪畫P點的軌跡圖

B) A及B的坐標分別為(-2,-6)及(7,3). X點移動時使得AX垂直於BX,繪畫軌跡圖

回答 (1)

用戶10012

2012-07-22 4:10 pm

✔ 最佳答案

A) Let P be (x,y). Distance between P and (-2,5) = sqrt [(x + 2)^2 + (y - 5)^2]
Distance between P and x - axis = y.
So sqrt [(x + 2)^2 + (y - 5)^2] = y
(x+ 2)^2 + (y - 5)^2 = y^2
(x + 2)^2 - 10y + 25 = 0
y = (x + 2)^2/10 + 5/2
So locus of P is a parabola with vertex ( - 2, 5/2).
B)
Let P be (x,y)
Slope of AX = (y +6)/(x + 2)
Slope of BX = (y - 3)/(x - 7)
Since AX is perpendicular to BX
so (y + 6)(y - 3)/(x + 2)(x - 7) = - 1
that is (x + 2)(x - 7) + (y + 6)(y - 3) = 0
Which is a circle with (-2, -6) and (7,3) as diameter (property of angle of semi - circle is 90 degree).

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