Maths - Ans.fyi 參考答案

Maths

2012-06-17 11:42 pm

1.It is given that y varies directly as the square root of x and inversely as z.

If y increases by 10% and z decreases by 20%,find the % change in x.

2.A(-1,3) abd B(1,-1) are two fixed points on the rectangular coodinate plane.If moving P(x,y) is the centre of the circle passing through points A and B,find the equation of the locus of P.

3.A moving pointP(x,y) and a fixed point G keeps a fixed distance a units apart.If the equation of the locus of P is x^2+y^2-8x+6y+16=0,
a)find the coordinate of G
b) find the value of a.

4.The equation of circle C is x^2+y^2=18 and the equation of straight line L is y=mx+6.
a)If L intersects C ,find the equation of L.

回答 (1)

tttfffkkk

2012-06-21 6:55 pm

✔ 最佳答案

圖片參考：http://upload.lyfhk.net/?pm=02I9
y=k√x/z
x=k'y²z²
x'=k'y'²z'²=k'(1.1y)²(0.8z)²=(1.1)²(0.8)²x
[(1.1)²(0.8)²-1]x100%/1=-22.56%

http://upload.lyfhk.net/?pm=02I9
mid-point of AB=(0,1)
slope of AB=-2
slope of locus=1/2
equation of locus:y=x/2+1

G=(4,-3)
a=√(4²+3²-16)=3

x²+y²=18 and y=mx+6
x²+(mx+6)²=18
(m²+1)x²+12mx+18=0
△=0
144m²-72m²-72=0
m=1 or -1
equation of L:y=x+6 or y=-x+6

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