已知圆:x²+y²-4x-6y+12=0,点A(3,5),点P(x,y)为圆上任意一点,求y /x的最值
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![已知圆:x²+y²-4x-6y+12=0,点A(3,5),点P(x,y)为圆上任意一点,求y /x的最值](/uploads/image/z/3776047-7-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%86%3Ax%26%23178%3B%2By%26%23178%3B-4x-6y%2B12%3D0%2C%E7%82%B9A%283%2C5%29%2C%E7%82%B9P%EF%BC%88x%2Cy%29%E4%B8%BA%E5%9C%86%E4%B8%8A%E4%BB%BB%E6%84%8F%E4%B8%80%E7%82%B9%2C%E6%B1%82y+%2Fx%E7%9A%84%E6%9C%80%E5%80%BC)
已知圆:x²+y²-4x-6y+12=0,点A(3,5),点P(x,y)为圆上任意一点,求y /x的最值
已知圆:x²+y²-4x-6y+12=0,点A(3,5),点P(x,y)为圆上任意一点,求y /x的最值
已知圆:x²+y²-4x-6y+12=0,点A(3,5),点P(x,y)为圆上任意一点,求y /x的最值
设y/x=k,y=kx代入圆方程中有:x^2+k^2x^2-4x-6kx+12=0
(1+k^2)x^2-(4+6k)x+12=0
判别式=(4+6k)^2-48(1+k^2)>=0
16+36k^2+48k-48-48k^2>=0
12k^2-48k+32