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) \[\frac{12}{7}\]

Correct Answer: A

Solution :

[a]

Equation of ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\]

\[\angle ACB=90{}^\circ \]

\[CA=4,CB=3\]

\[\Rightarrow \]\[\frac{1}{C{{A}^{2}}}+\frac{1}{C{{B}^{2}}}=\frac{1}{16}+\frac{1}{9}=\frac{25}{144}\]