If a hyperbola passes through the point P (10, 16), and it has...

Let the equation of hyperbola is $\dfrac{{x}^{2}}{{a}^{2}} - \dfrac{{y}^{2}}{{b}^{2}} = 1$.

As, vertex is at \left(\pm 6, 0\right)$, and it passes through \left(10, 16\right)$,
So, the equation of hyperbola is $\dfrac{{x}^{2}}{36} - \dfrac{{y}^{2}}{144} = 1$.
Equation of normal to the hyperbola at \left({x}_{1}, {y}_{1}\right)$is$\dfrac{{a}^{2}x}{{x}_{1}} + \dfrac{{b}^{2}y}{{y}_{1}} = {a}^{2} + {b}^{2}$</p><p>Thus, on putting values, equation of normal is$2x + 5y = 100$.