Let \(S\) and \({S}^{'}\) be the foci of the ellipse \(\frac{{x}^{2}}{25}+\frac{{y}^{2}}{9}=1\) and \(P(\alpha ,\text{ }…

Let \(S\) and \({S}^{'}\) be the foci of the ellipse \(\frac{{x}^{2}}{25}+\frac{{y}^{2}}{9}=1\) and \(P(\alpha ,\text{  }\beta )\) be a point on the ellipse in the first quadrant. If \({(SP)}^{2}+{({S}^{'}P)}^{2}−SP⋅{S}^{'}P=37,\) then \({\alpha }^{2}+{\beta }^{2}\) is equal to

[JEE Main 2026, 22 Jan (Shift 2)]