• # question_answer C is the centre of ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1$ and A and B are two points on the ellipse such that $\angle ACB=90{}^\circ ,$ then is equal to A) $\frac{25}{144}$          B) $\frac{144}{25}$ C) $\frac{7}{12}$                          D) $\frac{12}{7}$

[a]  Equation of ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1$ $\angle ACB=90{}^\circ$ $CA=4,CB=3$ $\Rightarrow$$\frac{1}{C{{A}^{2}}}+\frac{1}{C{{B}^{2}}}=\frac{1}{16}+\frac{1}{9}=\frac{25}{144}$