Question

Let the equation of the tangent to the hyperbola $16x^2-9y^2=144$ at $(5,\frac{16}{3})$ be $ax-by=k$ (in its simplest form). Find $k-(a+b)$

Answer 1

Required equation of tangent is given by, $T=0$
$\Rightarrow 16x\left(5\right)-9y\left(\frac{16}{3}\right)=144$
$\Rightarrow 5x-3y=9$

Then $k-(a+b)=9-(5+4)=1$