Let \[P(a\,\,sec\theta ,b\,\,tan\,\theta )\] and Q \[Q(a\,\,sec\,\phi ,\,\,b\,tan\,\,\phi ),\]where \[\theta +\phi =\pi /2,\] be two points on the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1.\] If \[(h,k)\] is the point of intersection of the normal at P and Q, then kz is equal to

• A. \[\frac{{{a}^{2}}+{{b}^{2}}}{a}\]
• B. \[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{a} \right)\]
• C. \[\frac{{{a}^{2}}+{{b}^{2}}}{b}\]
• D. \[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{b} \right)\]