A) \[p=\pm 1\]
B) \[p=\pm 2\]
C) \[p=\pm \frac{1}{2}\]
D) None of these
Correct Answer: D
Solution :
\[\frac{dy}{dx}=p{{e}^{px}}+p\]at point\[(0,\,\,1)=2p\] Subtangent\[=\left| y\frac{dy}{dx} \right|\], Subnormal\[=\left| y\frac{dy}{dx} \right|\] Given, Subtangent = Subnormal \[{{p}^{2}}=q\] \[\frac{dy}{dx}=\pm 1\] \[\Rightarrow \] \[2p=\pm 1\] \[\therefore \] \[p=\pm \frac{1}{2}\]
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