ρ^2=16cos2θ化为直角坐标方程.

显示全部楼层 · 2013-1-26 00:06:25

ρ^2=16cos2θρ^4=16ρ2cos2θρ^4=16ρ2cos2θρ^4=16ρ2（2cos2θ-1）（x2+y2）2=32x2-16（x2+y2）x^4+2x2y2+y^4=16x2-16y2x^4+2x2y2+y^4-16x2+16y2=0简化就是（x2+y2）2-16（x2-y2）=0...

千问 · 2013-1-26 00:06:25

解：x=ρcosθy=ρsinθ.x^2+y^2=ρ^2ρ^2=16cos2θ=16cos^2θ-16sin^2θ二边同乘以ρ^2ρ^4=16ρ^2cos^2θ-16ρ^2sin^2θρ^4=16(ρcosθ)^2-16(ρsinθ)^2(x^2+y^2)^2=16x^2-16y^2(x^2+y^2)^2－16(x^2-y...

千问 · 2013-1-26 00:06:25

ρ^2=x^2+y^2嘛cosθ=x/√(x^2+y^2)cos2θ=2(cosθ)^2-1=2x^2/(x^2+y^2)-1∴原式就是x2+y2=32x2/(x2+y2)-16(x2+y2)2 - 32x2 + 16(x2+y2)=0...