已知实数x y满足x^2+y^2-6x-8y+21=0,求y/x的取值范围,和x^2+Y^2+2x+4y的最值
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![已知实数x y满足x^2+y^2-6x-8y+21=0,求y/x的取值范围,和x^2+Y^2+2x+4y的最值](/uploads/image/z/3680081-17-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0x+y%E6%BB%A1%E8%B6%B3x%5E2%2By%5E2-6x-8y%2B21%3D0%2C%E6%B1%82y%2Fx%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%2C%E5%92%8Cx%5E2%2BY%5E2%2B2x%2B4y%E7%9A%84%E6%9C%80%E5%80%BC)
已知实数x y满足x^2+y^2-6x-8y+21=0,求y/x的取值范围,和x^2+Y^2+2x+4y的最值
已知实数x y满足x^2+y^2-6x-8y+21=0,求y/x的取值范围,和x^2+Y^2+2x+4y的最值
已知实数x y满足x^2+y^2-6x-8y+21=0,求y/x的取值范围,和x^2+Y^2+2x+4y的最值
因为x^2+y^2-6x-8y+21=0所以(x-3)^2+(y-4)=4,所以设x=2sina+3,y=2cosa+4,所以x^2+y^2+2x+4y=(2sina+3)^2+(2cosa+4)^2+2(2sina+3)+4(2cosa+4)=16sina+24cosa+51
=8√13[(2/√13)sina+(3/√13)cosa]+51
=(8√13)sin(a+θ)+51 (cosθ=2/√13,sinθ=3/√13)
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