参数方程与普通方程互化
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/11 11:02:01
参数方程与普通方程互化
x=2t/(1+t^2)
y=(1-t^2)/(1+t^2)
x=2t/(1+t^2)
y=(1-t^2)/(1+t^2)
![参数方程与普通方程互化](/uploads/image/z/15804329-41-9.jpg?t=%E5%8F%82%E6%95%B0%E6%96%B9%E7%A8%8B%E4%B8%8E%E6%99%AE%E9%80%9A%E6%96%B9%E7%A8%8B%E4%BA%92%E5%8C%96)
x=2t/(1+t^2)
y=(1-t^2)/(1+t^2)
x^2=4t^2/(1+t^2)^2
y^2=(1-t^2)^2/(1+t^2)^2
=(1-2t^2+t^4)/(1+t^2)^2
x^2+y^2
=[4t^2+1-2t^2+t^4]/(1+t^2)^2
=(t^2+1)^2/(1+t^2)^2
=1
所以该参数方程对应的普通方程是:
x^2+y^2=1
y=(1-t^2)/(1+t^2)
x^2=4t^2/(1+t^2)^2
y^2=(1-t^2)^2/(1+t^2)^2
=(1-2t^2+t^4)/(1+t^2)^2
x^2+y^2
=[4t^2+1-2t^2+t^4]/(1+t^2)^2
=(t^2+1)^2/(1+t^2)^2
=1
所以该参数方程对应的普通方程是:
x^2+y^2=1