中五 附加數學 --- Locus problems

(a)
x= 4t-1, y=t+3
y=(x+1)/4 +3
x-4y+13=0 a straight line
(b)
x = 4 cosØ, y = 3sinØ
sin²Ø+cos²Ø = (x/4)²+(y/3)²=1
x²/16+y²/9 =1 an elipse

(c )
x = 5secØ y = 3tanØ
sec²Ø – 1 = tan²Ø

(x/5)² -1 = (y/3)²
x²/25 – y²/9 =1 a hyperbraler

(d)
P(t*/2,t)

x= t² y = t
y²=x a parabola

Suppose x=cosθ and y=2+cos2θ.As θvaries,find an eqt connecting x and y.

y= 2 + cos2Ø = 2 + 2cos²Ø-1 = 2x² -1

y= 2x²-1

Suppose x=2(secθ+tanθ)and y=2(secθ-tanθ).As θvaries,find an eqt connecting x and y.

x=2(secθ+tanθ)
y=2(secθ-tanθ)

4secØ = x+y
4tanØ=x-y

sec²Ø-1 = tan²Ø

(x+y)²/16 –1 = (x-y)²/16

xy = 4

Suppose x=3t/(1+t^)and y=3t*/(1+t^).As t varies,find an eqt connecting x and y.

x=3t/(1+t³)

y=3t²/(1+t³)

y/x = t

x = 3(y/x) /(1 + (y/x)³)
x³ - 3xy + y³ =0

2006-10-15 23:42:30 補充：
a straight line 直線
an elipse 橢圓
a hyperbraler 雙曲線
a parabola 拋物線
你計得出方程式都要知道計緊乜！