A) \[y=3x-5\]
B) \[y=3x+5\]
C) \[y=3x+5\]and\[y=3x-5\]
D) None of the above
Correct Answer: C
Solution :
Given, hyperbola is\[2{{x}^{2}}-3{{y}^{2}}=6\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] \[\therefore \] \[{{a}^{2}}=3,{{b}^{2}}=2\] and \[y=3x+4\] \[\therefore \] \[m=3\] \[\therefore \]Equation of tangent is \[y=mx\pm \sqrt{({{a}^{2}}{{m}^{2}}-{{b}^{2}})}\] \[\Rightarrow \] \[y=3x\pm \sqrt{3.{{(3)}^{2}}-2}\] \[\Rightarrow \] \[y=3x\pm \sqrt{27-2}\] \[\therefore \] \[y=3x\pm 5\]
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