A) \[-\frac{4}{9}\]
B) \[-\frac{2}{9}\]
C) \[-\frac{1}{3}\]
D) 1
Correct Answer: A
Solution :
Given equation of curve is\[{{y}^{2}}={{x}^{3}}\] \[\Rightarrow \] \[2y=\frac{dy}{dx}=3{{x}^{2}}\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{3{{x}^{2}}}{2y}\] \[\therefore \] \[{{\frac{dy}{dx}}_{({{m}^{2}},{{m}^{3}})}}=\frac{3{{m}^{4}}}{2{{m}^{3}}}=\frac{3}{2}m\] and \[{{\frac{dy}{dx}}_{({{M}^{2}},{{M}^{3}})}}=\frac{3{{m}^{4}}}{2{{m}^{3}}}=\frac{3}{2}m\] Also, \[\frac{3}{2}m\times \frac{3}{2}M=-1\] \[\Rightarrow \] \[mM=-\frac{4}{9}\]You need to login to perform this action.
You will be redirected in
3 sec