Plz answer question before 9pm

👨🏻‍🏫 學術台數學

用戶85377

2009-05-02 4:07 am

Express the steps clearly.

1. Let A be the point (1, 4) and B be a variable point on the curve y^2 = 4x. Find the equation of the locus of the mid-point of AB.

Please show the steps clearly before 9 pm.

更新1:

Let B be (t^2, 2t). Why does the y-coordinate of y be 2t??

更新2:

Four minutes left.

回答 (3)

螞蟻雄兵

2009-05-02 4:14 am

✔ 最佳答案

1.Let A be the point (1, 4) and B be a variable point on the curve y^2 =4x. Find the equation of the locus of the mid-point of AB.
Sol
set B(a,b) then b^2=4a
2x=1+a,2y=4+b
b^2=4a
(2y-4)^2=4(2x-1)
(y-2)^2=(2x-1)
the locus of the mid-point of AB is (y-2)^2=(2x-1)

Please show the steps clearly before 9 pm.

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用戶7639

2009-05-02 4:27 am

Let B=(a,b),
the locus of the AB=M(x,y)。
x=(a+1)/2
a=2x-1
y=(b+4)/2
b=2y-4
B be a variable point on the curve y2 = 4x
∴ b2 = 4a
(2y-4)2 = 4(2x-1)
4y2-16y+16=8x-4
4y2-8x-16y+20=0
y2-2x-4y+5=0//

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用戶9170

2009-05-02 4:18 am

Let B be (t^2, 2t).

Mid-point of AB is ( (t^2 + 1)/2 , (2t + 4)/2 ).

Eliminate t, we get the locus of the mid-point of AB:

(y - 2)^2 = 2x - 1

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