实数x,y满足3x^2+2y^2=6x,求x^2+y^2的最小值和最大值高中参数方程过程
问题描述：
实数x,y满足3x^2+2y^2=6x,求x^2+y^2的最小值和最大值高中参数方程过程
答
3x^2+2y^2=6x
--->3(x^2-2x)^2+2y^2=0
--->3(x-1)^2+2y^2=3
--->(x-1)^2+y^2/(3/2)=1......(*)
--->x=1+cost; y=√(3/2)sint
因此x^2+y^2=(1+cost)^2+3/2*(sint)^2
=[1+2cost+(cost)^2]+3/2[1-(cost)^2]
=-1/2*(cost)^2+2cost+5/2
=-1/2*(cost-2)^2+9/2
-1=
答
3x^2+2y^2=6x3x^2-6x+3+2y^2=33(x-1)^2+2y^2=3(x-1)^2+(2/3)y^2=1令x-1=sina y=√(3/2)cosax^2+y^2=(1+sina)^2+(3/2)(cosa)^2=(sina)^2+2sina+1+(cosa)^2+(1/2)[1-(sina)^2]=-(sina)^2/2+2sina+5/2=(-1/2)[(sina)^2-...