Let S and S' be the foci of the ellipse x^2/25+y^2/9=1 and P (α, β) be a point on the ellipse in the first quadrant. If ( SP )^2+( S^′ P )^2- SP ·…

Let S and S' be the foci of the ellipse $\displaystyle \frac{x^2}{25}+\frac{y^2}{9}=1$ and $\displaystyle \mathrm{P}(\alpha, \beta)$ be a point on the ellipse in the first quadrant. If $\displaystyle (\mathrm{SP})^2+\left(\mathrm{S}^{\prime} \mathrm{P}\right)^2-\mathrm{SP} \cdot \mathrm{S}^{\prime} \mathrm{P}=37$, then $\displaystyle \alpha^2+\beta^2$ is equal to :