If PSP¹ is a focal chord of the ellipse $\frac{{\mathrm{x}}^2}{7}+\frac{{\mathrm{y}}^2}{9}=1\text{ then }\frac{\mathrm{SP}\cdot {\mathrm{SP}}^1}{\mathrm{SP}+{\mathrm{SP}}^1}=$

$$\begin{gathered} From given ellipse a^2=7,b=3 and PSP\text{'} is focal chord then \frac{1}{SP}+\frac{1}{SP\text{'}}=\frac{2}{l} \\ \frac{\mathrm{SP}\cdot {\mathrm{SP}}^{\mathrm{\prime }}}{\mathrm{SP}+{\mathrm{SP}}^{\mathrm{\prime }}}=\frac{1}{\frac{1}{\mathrm{SP}}+\frac{1}{{\mathrm{SP}}^{\mathrm{\prime }}}}=\frac{l}{2}=\frac{7}{6} where l=\frac{a^2}{b} \end{gathered}$$