A) \[3x+8y=50\]
B) \[3x-8y=50\]
C) \[8x+3y=50\]
D) \[8x-3y=50\]
Correct Answer: A
Solution :
Equation of normal at any point \[({{x}_{1}},{{y}_{1}})\] on hyperbola is, \[\frac{{{a}^{2}}(x-{{x}_{1}})}{{{x}_{1}}}=\frac{{{b}^{2}}(y-{{y}_{1}})}{-{{y}_{1}}}\] Here, \[{{a}^{2}}=267,\,{{b}^{2}}=48\] and \[({{x}_{1}},{{y}_{1}})=(6,4)\] \[\therefore \frac{27(x-6)}{6}=-\frac{48(y-4)}{4}\] Þ \[3(x-6)=-8(y-4)\] Þ \[3x+8y=50\].
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