若mρcos²θ+3ρsin²θ-6cosθ是椭圆,求m范围
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![若mρcos²θ+3ρsin²θ-6cosθ是椭圆,求m范围](/uploads/image/z/4502451-3-1.jpg?t=%E8%8B%A5m%CF%81cos%26%23178%3B%CE%B8%2B3%CF%81sin%26%23178%3B%CE%B8-6cos%CE%B8%E6%98%AF%E6%A4%AD%E5%9C%86%2C%E6%B1%82m%E8%8C%83%E5%9B%B4)
若mρcos²θ+3ρsin²θ-6cosθ是椭圆,求m范围
若mρcos²θ+3ρsin²θ-6cosθ是椭圆,求m范围
若mρcos²θ+3ρsin²θ-6cosθ是椭圆,求m范围
应该是mρcos²θ+3ρsin²θ-6cosθ=0是椭圆吧.
两边都乘以ρ,得mρ²cos²θ+3ρ²sin²θ-6ρcosθ=0
也即:
mx²+3y²-6x=0
变形得
(x-3/m)²/(9/m²)+y²/(3/m)=1
要使上式表示椭圆,必须3/m>0且9/m²≠3/m
得m>0且m≠3.