A) \[y=ax+b\]
B) \[{{y}^{2}}=2ax+2b\]
C) \[a{{y}^{2}}-{{x}^{3}}=a\]
D) None of these
Correct Answer: B
Solution :
Since, length of subnormal \[=a\] \[\Rightarrow \] \[y\frac{dy}{dx}=a\] \[\Rightarrow \] \[y\,dy=a\,dx\] On integrating both sides, we get \[\frac{{{y}^{2}}}{2}=ax+b,\] where b is a constant of integration \[\Rightarrow \] \[{{y}^{2}}=2ax+2b\]
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