先对等式a^2*X^2+b^2*y^2=a^2b^2求一阶导：
2*a^2*X+2*b^2*y*y’=0
y’=-a^2*X/(b^2*y)
再对2*a^2*X+2*b^2*y*y’=0求导：
2*a^2+2*b^2*(y’)^2+2*b^2*y*y"=0
2*a^2+2*b^2*(-a^2*X/(b^2*y))^2+2*b^2*y*y"=0
整理得
a^2+a^4*X^2/(b^2*y^2)+b^2*y*y"=0
将b^2*y^2=a^2b^2-a^2*X^2带入,得
b^2*y*y"=a^2+a^4*X^2/(a^2b^2-a^2*X^2)=a^2b^2/(b^2-X^2)
y"=a^2/(b^2-X^2)/y