question_answer

The locus of the feet of the perpendiculars drawn from either focus on a variable tangent to the hyperbola\[16{{y}^{2}}-9{{x}^{2}}=1\]is

A) \[{{x}^{2}}+{{y}^{2}}=9\]      

B) \[{{x}^{2}}+{{y}^{2}}=1/9\]

C) \[{{x}^{2}}+{{y}^{2}}=7/144\]

D) \[{{x}^{2}}+{{y}^{2}}=1/16\]

Correct Answer: D

Solution :

[d] \[\frac{{{y}^{2}}}{1/16}-\frac{{{x}^{2}}}{1/9}=1\] Locus will be the auxiliary circle \[{{x}^{2}}+{{y}^{2}}=\frac{1}{16}\]