若曲线的极坐标方程为ρ²=400/(16cos²θ+25sin²θ),这条曲线的普通方程是?
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若曲线的极坐标方程为ρ²=400/(16cos²θ+25sin²θ),这条曲线的普通方程是?
若曲线的极坐标方程为ρ²=400/(16cos²θ+25sin²θ),这条曲线的普通方程是?
若曲线的极坐标方程为ρ²=400/(16cos²θ+25sin²θ),这条曲线的普通方程是?
ρ²=x²+y² cos²θ=x²/ρ² sin²θ=y²/ρ² 代入ρ²=400/(16cos²θ+25sin²θ),
得ρ²=400/(16x²/ρ²+25y²/ρ²) 即 400=16x²+25y²
即16x²/400+25y²/400=1 化简得 x²/25+y²/16=1
这条曲线的普通方程为 x²/25+y²/16=1