A) \[3y=9x+2\]
B) \[y=2x+1\]
C) \[2y=x+8\]
D) \[y=x+2\]
Correct Answer: D
Solution :
Tangent to the curve\[{{y}^{2}}=8x\]is\[y=mx+\frac{2}{m}\]. So, it must satisfy\[xy=-1\] \[\Rightarrow \]\[x\left( mx+\frac{2}{m} \right)=-1\] \[\Rightarrow \] \[m{{x}^{2}}+\frac{2}{m}x+1=0\] Since, it has equal roots. \[\therefore \] \[D=0\] \[\Rightarrow \] \[\frac{4}{{{m}^{2}}}-4m=0\] \[\Rightarrow \] \[{{m}^{3}}=1\] \[\Rightarrow \] \[m=1\] So, equation of common tangent is\[y=x+2\].
You need to login to perform this action.
You will be redirected in
3 sec
