A) \[(-3,1)\] lies on the hyperbola
B) \[(3,1)\]lies on the hyperbola
C) \[(10,4)\]lies on the hyperbola
D) \[(5,2)\] lies on the hyperbola
Correct Answer: C
Solution :
Given, \[\frac{{{x}^{2}}}{36}-\frac{{{y}^{2}}}{{{k}^{2}}}=1\] \[\Rightarrow \] \[\frac{{{y}^{2}}}{{{k}^{2}}}=\frac{{{x}^{2}}}{36}-1\] \[\Rightarrow \] \[{{k}^{2}}=\frac{36{{y}^{2}}}{{{x}^{2}}-36}\] \[{{k}^{2}}>0\] if \[{{x}^{2}}-36>0\] \[\Rightarrow \] \[{{x}^{2}}>36\] This is true only for point \[(10,4)\]. So, \[(10,4)\]lies on the hyperbola.
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