数学F是椭圆5x^2+9y^2=
解：椭圆方程化为x^2/(1/5)+y^2/(1/9)=1,c^2=1/5-1/9=4/45,c=(2/15)√5。左焦点F为(-(2/15)√5，0),左准线为x=-(3√5)/10。e=2/3。 设P(x,y),则5x^2+9y^2=1。 (1)
对x求导得10x+18y*y’=0,y’=-5x/9y。 (2)
PF=(2/3)[x+(3√5)/10]
PA+PF=√[(x-1)^2+(y-1)^2]+(2/3)[x+(3√5)/10],记为w,
对x求导得w’=[x-...全部
解：椭圆方程化为x^2/(1/5)+y^2/(1/9)=1,c^2=1/5-1/9=4/45,c=(2/15)√5。左焦点F为(-(2/15)√5，0),左准线为x=-(3√5)/10。e=2/3。
设P(x,y),则5x^2+9y^2=1。 (1)
对x求导得10x+18y*y’=0,y’=-5x/9y。 (2)
PF=(2/3)[x+(3√5)/10]
PA+PF=√[(x-1)^2+(y-1)^2]+(2/3)[x+(3√5)/10],记为w,
对x求导得w’=[x-1+(y-1)y’]/√[(x-1)^2+(y-1)^2]+2/3
令w’=0,化简得3[x-1+(y-1)y’]=-2√[(x-1)^2+(y-1)^2]
两边平方，把(2)代入后得9[x-1-5x(y-1)/(9y)]^2=4[(x-1)^2+(y-1)^2],
9{(x-1)^2-10x(x-1)(y-1)/(9y)+25x^2*(y-1)^2/(81y^2)}=4[(x-1)^2+(y-1)^2]
两边都乘以9y^2,得81y^2*(x-1)^2-90xy(x-1)(y-1)+25x^2*(y-1)^2=36y^2*[(x-1)^2+(y-1)^2],
45y^2*(x-1)^2-90xy(x-1)(y-1)+25x^2*(y-1)^2-36y^2*(y-1)^2=0,
和(1)联立，求驻点坐标。
计算量太大了。恕不继续。
。收起
