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

$\text{ Since tangents drawn from the point }A(a,2)\text{ are perpendicular, }$

$A\text{ must lie on the director circle }{x}^2+y^2=\text{ 7. Putting }x=a\text{ and }y=2\text{ , }$

$\text{ we get the value of }{a}^2=3$