将参数方程:x=t⼀(1-2t^2),y=(1-2t^2)⼀(1+2t^2)化为一般方程

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2025-06-24 07:06:44
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回答1:

8x^2+1
=8t^2/(1-2t^2)^2 +1
=(8t^2+1-4t^2+4t^4)/(1-2t^2)^2
=(4t^2+1+4t^4)/(1-2t^2)^2
=(1+2t^2)^2/(1-2t^2)^2
=(1/y)^2

化为一般方程为
8x^2y^2+y^2=1