A) \[2y=x+8\]
B) \[y=x+2\]
C) \[y=2x+1\]
D) \[3y=9x+2\]
Correct Answer: B
Solution :
[b] Equation of the tangent of the curve \[{{y}^{2}}=8x\,be\,y=mx+\frac{2}{m}\] And it must satisfy the equation \[-xy=-1\] \[\Rightarrow x\left( mx+\frac{2}{m} \right)=-1\Rightarrow m{{x}^{2}}+\frac{2}{m}x+1=0\] Which is quadratic equation in x and its roots be equal. i.e. D=0 \[\Rightarrow {{b}^{2}}-4ac=0{{\left( \frac{2}{m} \right)}^{2}}-4.m.1=0\] \[\Rightarrow {{m}^{3}}=1\] \[\therefore m=1\] Hence, equation of the comment tangent be \[y=x+2\] Hence option [b] is correct.
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