A) \[y=3x-4\]
B) \[y=3x-5\]
C) \[y=3x+5\]
D) \[y=3x\pm 5\]
Correct Answer: D
Solution :
Given hyperbola is \[2{{x}^{2}}-3{{y}^{2}}=6\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] Here, \[{{a}^{2}}=3,\text{ }{{b}^{2}}=2\] Since, tangent is parallel to \[y=3x+4\] \[\therefore \] Here, \[m=3\] Thus, tangent of hyperbola is \[y=mx\ne \sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}}\] \[\Rightarrow \] \[y=3x\pm \sqrt{3.9-2}\] \[\Rightarrow \] \[y=3x\pm 5\]
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