question_answer

The point of contact of the line \[y=x-1\] with \[3{{x}^{2}}-4{{y}^{2}}=12\] is    [BIT Mesra 1996]

A)            (4, 3)                                         

B)            (3, 4)

C)            (4, ?3)                                       

D)            None of these

Correct Answer: A

Solution :

           The equation of the line and hyperbola are                   \[y=x-1\]                                                           .....(i)                   \[3{{x}^{2}}-4{{y}^{2}}=12\]                                                      .....(ii) From (i) and (ii), we get                   \[3{{x}^{2}}-4{{(x-1)}^{2}}=12\]                   \[\Rightarrow 3{{x}^{2}}-4({{x}^{2}}-2x+1)=12\]                   or \[{{x}^{2}}-8x+16=0\]Þ \[x=4\]                    From (i), \[y=3\]. So point of contact is\[(4,3)\].