Let \(A(2\sec { \theta } ,3\tan { \theta } )\) and \(B(2\sec { \phi } ,3\tan { \phi } )\) where \(\theta +\phi =\cfrac {…

Let \(A(2\sec { \theta } ,3\tan { \theta } )\) and \(B(2\sec { \phi } ,3\tan { \phi } )\) where \(\theta +\phi =\cfrac { \pi }{ 2 } \), be two points on the hyperbola \(\cfrac { { x }^{ 2 } }{ 4 } -\cfrac { { y }^{ 2 } }{ 9 } =1\). If \(\left( \alpha ,\beta \right) \) is the point of intersection of normals to the hyperbola at \(A\) and \(B\), then \(\beta=\)