A) \[4x+2y+1=0\]
B) \[x+2y+4=0\]
C) \[x+y+1=0\]
D) \[x-2y+4=0\]
Correct Answer: B
Solution :
Let the equation of tangent to parabola\[{{y}^{2}}=4x\]be \[y=mx+\frac{1}{m}\] ...(i) It is also a tangent to hyperbola xy = 2. \[\Rightarrow \]\[x\left( mx+\frac{1}{m} \right)=2\] [From (i)] \[\Rightarrow \]\[{{x}^{2}}m+\frac{x}{m}-2=0\] Now, D = 0 \[\Rightarrow \]\[\frac{1}{{{m}^{2}}}+8m=0\Rightarrow m=-\frac{1}{2}\] ?(iii) \[\therefore \]Equation of tangent is \[y=-\frac{1}{2}x-2\]\[\Rightarrow \]\[2y+x+4=0\]
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