If tangents drawn from the point (a, 2) to the hyperbola $\frac{{\mathrm{x}}^2}{16}-\frac{{\mathrm{y}}^2}{9}=1$are perpendicular, then the value of a² is 

Since tangents drawn from the point A(a,2) are perpendicular, A must lie on the director circle x² + y² =7. 
Putting y = 2,we get x²= a² = 3.