参数方程与普通方程的互化问题1、将参数方程 x=sinφ,(φ为参数)化为普通方程{y=cos2φ2、将参数方程x=(2-3t)/(1+t),(t为参数)化为普通方程,它表示的图形是：{y=(1+4t)/(1+t)3、x=(k+1)/(k+2)(k为参数)化为普通方程{y=(2k+1)/(k+2)4、x=3t/(1+t^2)(t为参数)化为普通方程{y=3t^2/(1+t^2)5、x=sinθ+cosθ(θ为参数){y=sinθ^3+cosθ^36、x=a(1-t^2)/(1+t^2)（t为参数）{y=2at/(1+t^2)格式不太好

1.y + 2x^2=1
2.5y+3x=11 斜率为-3/5 截距为11/5 的直线
3.y=3x-1
4.x^2=3y-y^2
5.2y=3x-x^3
6.x^2 + y^2 =a^2

1、
cos2φ=1-2(sinφ)^2
所以y=1-2x^2
2、
x=-(3t-2)/(t+1)=-(3t+3-5)/(t+1)=-3+5/(t+1)
y=(4t+1)/(t+1)=(4t+4-3)/(t+1)=4+3/(t+1)
所以3x-5y=-9+15/(t+1)+20-15/(t+1)
3x-5y-11=0
3、
x=(k+2-1)/(k+2)=1-1/(k+2)
y=(2k+4-3)/(k+2)=2-3/(k+2)
3x-y=3-3/(k+2)-2+3/(k+2)
3x-y-1=0
4、
y/x=t
所以x=3(y/x)/[1+(y/x)^2]=3xy/(x^2+y^2)
x^2+y^2-3y=0
5、
y=sinθ^3+cosθ^3
=(sinθ+cosθ)(sinθ^2-sinθcosθ+cosθ^2)
=x(1-sinθcosθ)
x=sinθ+cosθ
x^2=sinθ^2+2sinθcosθ+cosθ^2=1+2sinθcosθ
sinθcosθ=(x^2-1)/2
所以y=x[1-(x^2-1)/2]
y=-x^3/2+x-x/2
6、
(x/a)^2=(1-2t^2+t^4)/(1+t^2)^2
(y/a)^2=4t^2/(1+t^2)^2
(x/a)^2+(y/a)^2=(1+2t^2+t^4)/(1+t^2)^2=1
x^2/a^2+y^2/a^2=1

(1) y=cos2φ=1-2(sinφ)^2=1-2x^2
(2) x=(2-3t)/(1+t)=(5-3(1+t))/(1+t)=(5/(1+t))-3
y=(1+4t)/(1+t)=(4(1+t)-3)/(1+t)=4-(3/(1+t))
3x+5y=11
(3) x=(k+1)/(k+2)=1-(1/(k+2))
y=(2k+1)/(k+2)=2-(3/(k+2))
3x-y=1
(4) x=3t/(1+t^2)=(3t^2/(1+t^2))/t=y/t
t=y/x,代入x=3t/(1+t^2),得:
x=3(y/x)/(1+(y/x)^2)
x^2+y^2-3y=0
(5) y=sinθ^3+cosθ^3 =(sinθ+cosθ)(sinθ^2-sinθcosθ+cosθ^2)
=(sinθ+cosθ)(1-sinθcosθ)=x(1-sinθcosθ)
sinθcosθ=1-(y/x)
x^2=(sinθ+cosθ)^2=sinθ^2+cosθ^2+2sinθcosθ=1+2sinθcosθ=1+2(1-(y/x))
x^3-3x+2y=0
(6) x=a(1-t^2)/(1+t^2)=(2a/(1+t^2))-a=(y/t)-a
t=y/(x+a),代入y=2at/(1+t^2),得:
y=(2ay/(x+a))/(1+(y/(x+a))^2)
x^2+y^2=a^2