If $f:R\to \left[-1,2\right]$, $\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{x}}^2+9\mathrm{bx}+17}{{\mathrm{ax}}^3+{\mathrm{x}}^2+\mathrm{bx}+33}$ is onto function and $f\text{'}\left(d\right)=f\text{'}\left(e\right)=0$ . Then

eccentricity of curve $\frac{{\mathrm{x}}^2}{(\mathrm{d}+\mathrm{e}{)}^2}+\frac{{\mathrm{y}}^2}{\mathrm{b}+1}=1$ can be $\frac{1}{2}$

eccentricity of curve $\frac{{\mathrm{x}}^2}{(\mathrm{d}+\mathrm{e}{)}^2}+\frac{{\mathrm{y}}^2}{\mathrm{a}+1}=1$ can be $\frac{\sqrt{7}}{2}$

eccentricity of curve $\frac{{\mathrm{x}}^2}{(\mathrm{d}+\mathrm{e}{)}^2}+\frac{{\mathrm{y}}^2}{\mathrm{b}+1}=1$ can be $\frac{\sqrt{5}}{2}$

eccentricity of curve $\frac{{\mathrm{x}}^2}{(\mathrm{d}+\mathrm{e}{)}^2}+\frac{{\mathrm{y}}^2}{\mathrm{a}+1}=1$ can be $\frac{\sqrt{3}}{2}$