参数方程x=2+sin2θy=−1+cos2θ(θ为参数)化为普通方程是( ) A.2x-y+4=0 B.2x+y-4=0 C.2x-y+4=0,x∈[2,3] D.2x+y-4=0,x∈[2,3]
问题描述:
参数方程
(θ为参数)化为普通方程是( )
x=2+sin2θ y=−1+cos2θ
A. 2x-y+4=0
B. 2x+y-4=0
C. 2x-y+4=0,x∈[2,3]
D. 2x+y-4=0,x∈[2,3]
答
由条件可得 cos2θ=y+1=1-2sin2θ=1-2(x-2),
化简可得2x+y-4=0,x∈[2,3],
故选D.