A) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\]
B) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\]
C) \[{{x}^{2}}+{{y}^{2}}=2ab\]
D) None of these
Correct Answer: B
Solution :
Equation of hyperbola is \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] Any tangent to hyperbola are \[y=mx\pm \sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}}\] Also tangent perpendicular to this is \[y=\frac{-1}{m}x\pm \sqrt{\frac{{{a}^{2}}}{{{m}^{2}}}-{{b}^{2}}}\] Eliminating m, we get \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\].
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